Chapter 2 of 14
Chapter 2: Shapes and Angles
आकृतियाँ और कोण (माचिस की तीलियाँ, कोण टेस्टर एवं डिग्री घड़ी) | CBSE Session 2026–27
Core Pedagogical Competencies & Concepts
- Open and closed geometric shapes made of matchsticks (triangles, quadrilaterals, pentagons, hexagons).
- Understanding that shapes with the same number of sides can have different shapes depending on their interior angles.
- Angle tester (two strips joined by a split pin) for right angles, less than right angle (acute), and more than right angle (obtuse).
- The Degree Clock: identifying 45°, 90°, 180° through hands and turns.
- (a) 9:00: The hour hand is at 9 and the minute hand is at 12. Angle = $3 \times 30^\circ = 90^\circ$ → Right Angle.
- (b) 3:30: The hour hand is halfway between 3 and 4, and minute hand is at 6. Angle = $75^\circ$ → Less than a right angle (Acute Angle).
- (c) 7:15: The hour hand is just past 7 and minute hand is at 3. Angle = approx $127.5^\circ$ → More than a right angle (Obtuse Angle).
- (d) 2:00: The hour hand is at 2 and minute hand is at 12. Angle = $2 \times 30^\circ = 60^\circ$ → Less than a right angle (Acute Angle).
- (e) 6:00: The hour hand is at 6 and minute hand is at 12. Angle = $180^\circ$ → More than a right angle (Straight Angle).
- M: 3 angles (all 3 acute, less than right angle).
- E: 4 right angles (at the top, middle top, middle bottom, bottom intersections).
- E: 4 right angles.
- N: 2 angles (both acute, less than right angle).
- A: 3 acute angles (at the apex and crossbar) + 2 obtuse angles (below crossbar).
All Textbook Exercises & In-Text Tasks (24 Questions)
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Q1
Textbook Exercise • Matchstick Shapes & Angles
Rohini and Mohini made closed shapes with 6 matchsticks. Rohini made a regular hexagon, while Mohini made a closed 6-sided shape with two points pointing inwards. (a) Do both shapes have the same number of sides? (b) Are the angles in both shapes the same? Explain why.
[3 Marks]
✅ Step-by-Step Solution & Working
Explanation:
• (a) Sides: Yes, both shapes have exactly 6 sides because both used 6 matchsticks.
• (b) Angles: No, the angles are not the same. Even though the number of sides is identical, changing the orientation or slants of the matchsticks changes the internal angles between them. Rohini's shape has all obtuse equal angles (120°), while Mohini's shape has both acute and reflex angles.
• (a) Sides: Yes, both shapes have exactly 6 sides because both used 6 matchsticks.
• (b) Angles: No, the angles are not the same. Even though the number of sides is identical, changing the orientation or slants of the matchsticks changes the internal angles between them. Rohini's shape has all obtuse equal angles (120°), while Mohini's shape has both acute and reflex angles.
CBSE Step-by-Step Marking Scheme
Part (a): Yes, 6 sides
1 M
Part (b): No, angles differ due to slants
2 M
Q2
Textbook Exercise • Types of Angles
Define and give the degree range for: (a) Right Angle (b) Acute Angle (c) Obtuse Angle. Mention one real-life example for each.
[3 Marks]
✅ Step-by-Step Solution & Working
Definitions and Examples:
• (a) Right Angle: An angle exactly equal to 90° (forms an 'L' shape). Example: Corner of a book or door.
• (b) Acute Angle: An angle less than 90° (between 0° and 90°). Example: Open blades of scissors or hands of a clock at 2:00.
• (c) Obtuse Angle: An angle more than 90° and less than 180°. Example: Hands of a clock at 5:00 or a reclining lounge chair.
• (a) Right Angle: An angle exactly equal to 90° (forms an 'L' shape). Example: Corner of a book or door.
• (b) Acute Angle: An angle less than 90° (between 0° and 90°). Example: Open blades of scissors or hands of a clock at 2:00.
• (c) Obtuse Angle: An angle more than 90° and less than 180°. Example: Hands of a clock at 5:00 or a reclining lounge chair.
CBSE Step-by-Step Marking Scheme
Right angle definition & example
1 M
Acute angle definition & example
1 M
Obtuse angle definition & example
1 M
Q3
Textbook Exercise • Angles in Alphabet Letters
In the name word 'SUKHMAN', count and list the types of angles formed in the letters:
(a) In letter 'H', how many right angles are there?
(b) In letter 'N', what kind of angles are formed?
(c) In letter 'A', how many acute angles are inside the upper triangle?
[3 Marks]
(a) In letter 'H', how many right angles are there?
(b) In letter 'N', what kind of angles are formed?
(c) In letter 'A', how many acute angles are inside the upper triangle?
✅ Step-by-Step Solution & Working
Letter Analysis:
• (a) Letter 'H': There are 4 right angles (90°) where the horizontal crossbar meets the two vertical lines.
• (b) Letter 'N': There are 2 acute angles (both less than 90°) between the vertical lines and the diagonal slash.
• (c) Letter 'A': Inside the upper triangle of 'A', all 3 angles are acute angles (each less than 90°).
• (a) Letter 'H': There are 4 right angles (90°) where the horizontal crossbar meets the two vertical lines.
• (b) Letter 'N': There are 2 acute angles (both less than 90°) between the vertical lines and the diagonal slash.
• (c) Letter 'A': Inside the upper triangle of 'A', all 3 angles are acute angles (each less than 90°).
CBSE Step-by-Step Marking Scheme
Part (a): 4 right angles
1 M
Part (b): 2 acute angles
1 M
Part (c): 3 acute angles
1 M
Q4
Textbook Exercise • Clock Hands & Angles
Write what kind of angle (Right, Acute, or Obtuse) is made by the hands of a clock at the following times:
(a) 9:00
(b) 2:00
(c) 4:30
(d) 8:15
[4 Marks]
(a) 9:00
(b) 2:00
(c) 4:30
(d) 8:15
✅ Step-by-Step Solution & Working
Clock Angle Determinations:
• (a) 9:00: Exactly 3 hour divisions apart (3 × 30° = 90°). Angle: Right Angle.
• (b) 2:00: 2 hour divisions apart (2 × 30° = 60°). Angle: Acute Angle (less than 90°).
• (c) 4:30: Hour hand between 4 and 5, minute hand at 6. Gap is 1.5 divisions (1.5 × 30° = 45°). Angle: Acute Angle.
• (d) 8:15: Gap is about 5.25 divisions (approx 157.5°). Angle: Obtuse Angle (more than 90°).
• (a) 9:00: Exactly 3 hour divisions apart (3 × 30° = 90°). Angle: Right Angle.
• (b) 2:00: 2 hour divisions apart (2 × 30° = 60°). Angle: Acute Angle (less than 90°).
• (c) 4:30: Hour hand between 4 and 5, minute hand at 6. Gap is 1.5 divisions (1.5 × 30° = 45°). Angle: Acute Angle.
• (d) 8:15: Gap is about 5.25 divisions (approx 157.5°). Angle: Obtuse Angle (more than 90°).
CBSE Step-by-Step Marking Scheme
9:00 - Right angle
1 M
2:00 - Acute angle
1 M
4:30 - Acute angle
1 M
8:15 - Obtuse angle
1 M
Q5
Textbook Exercise • Angle Tester (Divider)
(a) What instrument from your geometry box can be used as an 'Angle Tester'? (b) How can you make a simple angle tester using two strips of cardboard and a drawing pin?
[3 Marks]
✅ Step-by-Step Solution & Working
Angle Tester Instructions:
• (a) Instrument: The Divider (an instrument with two pointed metal legs hinged together) acts as an angle tester.
• (b) DIY Cardboard Tester: Cut two equal strips of stiff cardboard (about 15 cm long and 2 cm wide). Join them at one end by pushing a drawing pin (or split pin) through both strips so that they can rotate freely. When the strips open like the letter 'L', it tests a right angle.
• (a) Instrument: The Divider (an instrument with two pointed metal legs hinged together) acts as an angle tester.
• (b) DIY Cardboard Tester: Cut two equal strips of stiff cardboard (about 15 cm long and 2 cm wide). Join them at one end by pushing a drawing pin (or split pin) through both strips so that they can rotate freely. When the strips open like the letter 'L', it tests a right angle.
CBSE Step-by-Step Marking Scheme
Part (a): Divider named
1 M
Part (b): Cardboard and pin method explained
2 M
Q6
Textbook Exercise • Degree Clock & Turns
A degree clock is divided into 360 degrees. (a) How many degrees are there in a 1/4 turn? (b) How many degrees are there in a 1/2 turn? (c) How many degrees are there in a 3/4 turn?
[3 Marks]
✅ Step-by-Step Solution & Working
Fractional Turns in Degrees:
• (a) 1/4 turn: 1/4 × 360° = 90° (Right angle).
• (b) 1/2 turn: 1/2 × 360° = 180° (Straight angle).
• (c) 3/4 turn: 3/4 × 360° = 270°.
• (a) 1/4 turn: 1/4 × 360° = 90° (Right angle).
• (b) 1/2 turn: 1/2 × 360° = 180° (Straight angle).
• (c) 3/4 turn: 3/4 × 360° = 270°.
CBSE Step-by-Step Marking Scheme
1/4 turn = 90°
1 M
1/2 turn = 180°
1 M
3/4 turn = 270°
1 M
Q7
Textbook Exercise • Yoga Asanas & Body Angles
Look at the angles made by the body in these yoga poses:
(a) In 'Dandasana' (sitting straight with legs stretched forward flat on ground), what angle does the back make with the legs?
(b) In 'Adho Mukha Svanasana' (Downwards Dog pose forming an inverted V), what type of angle is formed at the hips?
(c) When raising one arm straight overhead from the side, through what angle does the arm turn?
[3 Marks]
(a) In 'Dandasana' (sitting straight with legs stretched forward flat on ground), what angle does the back make with the legs?
(b) In 'Adho Mukha Svanasana' (Downwards Dog pose forming an inverted V), what type of angle is formed at the hips?
(c) When raising one arm straight overhead from the side, through what angle does the arm turn?
✅ Step-by-Step Solution & Working
Body Angles in Yoga:
• (a) Dandasana: The spine is perpendicular to the legs, making a Right Angle (90°).
• (b) Downward Dog pose: The torso and legs meet at the hip joint forming an angle less than 90°, which is an Acute Angle.
• (c) Overhead arm raise: Turning arm from side (downwards) to straight overhead is a half-circle turn of 180°.
• (a) Dandasana: The spine is perpendicular to the legs, making a Right Angle (90°).
• (b) Downward Dog pose: The torso and legs meet at the hip joint forming an angle less than 90°, which is an Acute Angle.
• (c) Overhead arm raise: Turning arm from side (downwards) to straight overhead is a half-circle turn of 180°.
CBSE Step-by-Step Marking Scheme
Part (a): Right angle (90°)
1 M
Part (b): Acute angle (<90°)
1 M
Part (c): 180° turn
1 M
Q8
Textbook Exercise • Carrom Board & Angles
On a carrom board, a player hits the striker from the baseline towards the opposite frame to pocket a queen in the side pocket. (a) What rule governs the angle at which the striker bounces off the edge? (b) If the striker hits the rim at 45°, at what angle will it rebound?
[2 Marks]
✅ Step-by-Step Solution & Working
Angle of Reflection:
• (a) Rule: The angle at which the striker hits the edge (angle of incidence) is equal to the angle at which it rebounds (angle of reflection). Both angles made with the perpendicular (normal) are equal.
• (b) Rebound angle: If it hits the edge at 45°, it will rebound at an angle of 45°.
• (a) Rule: The angle at which the striker hits the edge (angle of incidence) is equal to the angle at which it rebounds (angle of reflection). Both angles made with the perpendicular (normal) are equal.
• (b) Rebound angle: If it hits the edge at 45°, it will rebound at an angle of 45°.
CBSE Step-by-Step Marking Scheme
Part (a): Law of equal reflection angles
1 M
Part (b): 45° rebound
1 M
Q9
Textbook Exercise • Matchstick Puzzles
Take 8 matchsticks. (a) How can you arrange them to make a shape with 8 sides (octagon)? (b) Take 6 matchsticks and make a triangle. What kind of triangle is formed, and what can you say about its three angles?
[3 Marks]
✅ Step-by-Step Solution & Working
Matchstick Solutions:
• (a) 8 Matchsticks: Arrange the 8 matchsticks tip-to-tail in a closed loop with all equal interior angles. This forms a regular Octagon where all interior angles are obtuse (135° each).
• (b) 6 Matchsticks Triangle: Use 2 matchsticks on each side (2 + 2 + 2 = 6). An Equilateral Triangle is formed. All three angles are equal, acute, and measure exactly 60° each.
• (a) 8 Matchsticks: Arrange the 8 matchsticks tip-to-tail in a closed loop with all equal interior angles. This forms a regular Octagon where all interior angles are obtuse (135° each).
• (b) 6 Matchsticks Triangle: Use 2 matchsticks on each side (2 + 2 + 2 = 6). An Equilateral Triangle is formed. All three angles are equal, acute, and measure exactly 60° each.
CBSE Step-by-Step Marking Scheme
Part (a): Octagon description
1.5 M
Part (b): Equilateral triangle, 60° angles
1.5 M
Q10
Textbook Exercise • Measuring Angles on a Protractor
State whether the following angles are Acute, Right, or Obtuse: (a) 35° (b) 90° (c) 115° (d) 89° (e) 175° (f) 91°.
[3 Marks]
✅ Step-by-Step Solution & Working
Classification:
• (a) 35°: Acute angle (less than 90°)
• (b) 90°: Right angle (exactly 90°)
• (c) 115°: Obtuse angle (between 90° and 180°)
• (d) 89°: Acute angle (just less than 90°)
• (e) 175°: Obtuse angle (between 90° and 180°)
• (f) 91°: Obtuse angle (greater than 90°)
• (a) 35°: Acute angle (less than 90°)
• (b) 90°: Right angle (exactly 90°)
• (c) 115°: Obtuse angle (between 90° and 180°)
• (d) 89°: Acute angle (just less than 90°)
• (e) 175°: Obtuse angle (between 90° and 180°)
• (f) 91°: Obtuse angle (greater than 90°)
CBSE Step-by-Step Marking Scheme
All 6 classifications correct
3 M (0.5 M each)
Q11
Textbook Exercise • Open & Closed Shapes
Explain the difference between an 'Open Shape' and a 'Closed Shape'. Can an open shape have an internal area? Give an example of each.
[3 Marks]
✅ Step-by-Step Solution & Working
Explanation:
• Closed Shape: A figure that begins and ends at the exact same point, enclosing a bounded boundary. Example: Circle, square, triangle. It has an internal area.
• Open Shape: A figure where the starting point and ending point do not meet, leaving a gap. Example: Letter 'C' or 'U'. It does NOT have an internal area because it does not enclose a region.
• Closed Shape: A figure that begins and ends at the exact same point, enclosing a bounded boundary. Example: Circle, square, triangle. It has an internal area.
• Open Shape: A figure where the starting point and ending point do not meet, leaving a gap. Example: Letter 'C' or 'U'. It does NOT have an internal area because it does not enclose a region.
CBSE Step-by-Step Marking Scheme
Closed shape definition and example
1.5 M
Open shape definition and no area explanation
1.5 M
Q12
Textbook Exercise • Changing Shapes Changing Angles
If you push the corners of a matchstick square, it turns into a rhombus. (a) Do the lengths of the sides change? (b) Do the angles change? (c) Why are triangular structures used in building bridges and electricity towers instead of square structures?
[3 Marks]
✅ Step-by-Step Solution & Working
Structural Properties:
• (a) Side lengths: No, the side lengths remain the same because the matchsticks do not stretch or shrink.
• (b) Angles: Yes, the right angles (90°) change into two acute angles and two obtuse angles.
• (c) Triangle rigidity: A triangle is a rigid shape; its angles cannot change without changing the lengths of its sides. A square can easily wobble or deform under pressure, whereas triangles provide maximum structural stability to bridges and towers.
• (a) Side lengths: No, the side lengths remain the same because the matchsticks do not stretch or shrink.
• (b) Angles: Yes, the right angles (90°) change into two acute angles and two obtuse angles.
• (c) Triangle rigidity: A triangle is a rigid shape; its angles cannot change without changing the lengths of its sides. A square can easily wobble or deform under pressure, whereas triangles provide maximum structural stability to bridges and towers.
CBSE Step-by-Step Marking Scheme
Parts (a) and (b) answers
1 M
Part (c): Triangle rigidity explanation
2 M
Q13
Textbook Exercise • Scissors Blade Angles
Observe a pair of scissors: (a) What happens to the angle between the blades when the handles are pushed further apart? (b) If you cut thick cloth, should the angle between the blades be small (acute) or wide (obtuse) for best cutting power?
[2 Marks]
✅ Step-by-Step Solution & Working
Observation:
• (a) Angle change: When handles are opened wider, the angle between the blades increases.
• (b) Cutting power: A small acute angle near the pivot gives the greatest mechanical advantage and cutting pressure for thick cloth.
• (a) Angle change: When handles are opened wider, the angle between the blades increases.
• (b) Cutting power: A small acute angle near the pivot gives the greatest mechanical advantage and cutting pressure for thick cloth.
CBSE Step-by-Step Marking Scheme
Part (a): Angle increases
1 M
Part (b): Small acute angle near pivot
1 M
Q14
Textbook Exercise • Angle Sum of Triangles
A triangle has three angles. (a) What is the sum of all three angles of any triangle? (b) If one angle of a right-angled triangle is 40°, what is the third angle?
[3 Marks]
✅ Step-by-Step Solution & Working
Angle Sum Calculation:
• (a) Angle sum: The sum of the angles of any triangle is always 180°.
• (b) Third angle:
- In a right-angled triangle, one angle is 90°.
- Given second angle = 40°.
- Third angle = 180° - (90° + 40°) = 180° - 130° = 50°.
• (a) Angle sum: The sum of the angles of any triangle is always 180°.
• (b) Third angle:
- In a right-angled triangle, one angle is 90°.
- Given second angle = 40°.
- Third angle = 180° - (90° + 40°) = 180° - 130° = 50°.
CBSE Step-by-Step Marking Scheme
Sum of angles = 180°
1 M
Calculation showing 180 - 130 = 50°
2 M
Q15
Textbook Exercise • Roof Angles & Rain Drainage
Houses in hilly areas have sloped roofs. (a) Is the angle between the two sloping sides of the roof acute, right, or obtuse? (b) Why are sloped roofs preferred over flat roofs in regions with heavy snowfall?
[2 Marks]
✅ Step-by-Step Solution & Working
Reasoning:
• (a) Angle: The apex angle at the top ridge of the roof is typically an acute or right angle (steep pitch).
• (b) Purpose: The steep sloping angle prevents snow and rainwater from accumulating on the roof. Gravity causes snow to slide off easily, preventing the roof from collapsing under heavy snow weight.
• (a) Angle: The apex angle at the top ridge of the roof is typically an acute or right angle (steep pitch).
• (b) Purpose: The steep sloping angle prevents snow and rainwater from accumulating on the roof. Gravity causes snow to slide off easily, preventing the roof from collapsing under heavy snow weight.
CBSE Step-by-Step Marking Scheme
Part (a): Angle identified
1 M
Part (b): Snow sliding explanation
1 M
Q16
Textbook Exercise • Complementary Angles
Two angles are called complementary if their sum is 90°. Find the complement of: (a) 30° (b) 65° (c) 45°.
[3 Marks]
✅ Step-by-Step Solution & Working
Calculations:
• (a) Complement of 30° = 90° - 30° = 60°.
• (b) Complement of 65° = 90° - 65° = 25°.
• (c) Complement of 45° = 90° - 45° = 45°.
• (a) Complement of 30° = 90° - 30° = 60°.
• (b) Complement of 65° = 90° - 65° = 25°.
• (c) Complement of 45° = 90° - 45° = 45°.
CBSE Step-by-Step Marking Scheme
Part (a): 60°
1 M
Part (b): 25°
1 M
Part (c): 45°
1 M
Q17
Textbook Exercise • Clock Hand Movement in 1 Hour
In one full hour (60 minutes): (a) Through how many degrees does the minute hand turn? (b) Through how many degrees does the hour hand turn?
[2 Marks]
✅ Step-by-Step Solution & Working
Clock Rotations:
• (a) Minute hand: Completes 1 full circular turn in 60 minutes = 360°.
• (b) Hour hand: Moves from one number to the next (e.g. from 12 to 1). There are 12 divisions on clock face: 360° ÷ 12 = 30°.
• (a) Minute hand: Completes 1 full circular turn in 60 minutes = 360°.
• (b) Hour hand: Moves from one number to the next (e.g. from 12 to 1). There are 12 divisions on clock face: 360° ÷ 12 = 30°.
CBSE Step-by-Step Marking Scheme
Minute hand: 360°
1 M
Hour hand: 30°
1 M
Q18
Textbook Exercise • Finding Right Angles in Classroom
Name four objects in your classroom that have right angles at their corners.
[2 Marks]
✅ Step-by-Step Solution & Working
Classroom Examples:
1. The blackboard / whiteboard frame corners.
2. The classroom door and window frames.
3. The surface corners of the teacher's table / student desks.
4. The pages and cover of a textbook or notebook.
1. The blackboard / whiteboard frame corners.
2. The classroom door and window frames.
3. The surface corners of the teacher's table / student desks.
4. The pages and cover of a textbook or notebook.
CBSE Step-by-Step Marking Scheme
Four valid objects named (0.5 M each)
2 M
Q19
Textbook Exercise • Straight Angle & Reflex Angle
(a) What is the measure of a straight angle? (b) How many right angles make a straight angle? (c) What is an angle called if its measure is more than 180° but less than 360°?
[3 Marks]
✅ Step-by-Step Solution & Working
Angle Classifications:
• (a) Measure: A straight angle measures exactly 180°.
• (b) Number of right angles: 180° ÷ 90° = 2 right angles.
• (c) Angle name: An angle between 180° and 360° is called a Reflex Angle.
• (a) Measure: A straight angle measures exactly 180°.
• (b) Number of right angles: 180° ÷ 90° = 2 right angles.
• (c) Angle name: An angle between 180° and 360° is called a Reflex Angle.
CBSE Step-by-Step Marking Scheme
Part (a): 180°
1 M
Part (b): 2 right angles
1 M
Part (c): Reflex angle
1 M
Q20
Textbook Exercise • Angle of Elevation (Sun & Shadows)
At 12:00 noon, when the sun is directly overhead, what angle does a vertical pole make with the horizontal ground? What happens to the length of the shadow as the sun sets in the evening?
[2 Marks]
✅ Step-by-Step Solution & Working
Sun & Shadows:
• (a) Angle: A vertical pole makes a Right Angle (90°) with the horizontal ground.
• (b) Shadow behavior: As the sun descends lower towards the horizon in the evening, the angle of the sun's rays becomes smaller (acute), causing the shadow to become longer and longer.
• (a) Angle: A vertical pole makes a Right Angle (90°) with the horizontal ground.
• (b) Shadow behavior: As the sun descends lower towards the horizon in the evening, the angle of the sun's rays becomes smaller (acute), causing the shadow to become longer and longer.
CBSE Step-by-Step Marking Scheme
Right angle (90°)
1 M
Shadow becomes longer explanation
1 M
Q21
Textbook Exercise • Hands of Clock at 6:00
At 6:00: (a) What type of angle is formed between the hour hand and minute hand? (b) What is its exact degree measurement?
[2 Marks]
✅ Step-by-Step Solution & Working
Clock Analysis at 6:00:
• (a) Angle type: The hands point in exactly opposite directions along a straight line, forming a Straight Angle.
• (b) Degree measure: Exactly 180°.
• (a) Angle type: The hands point in exactly opposite directions along a straight line, forming a Straight Angle.
• (b) Degree measure: Exactly 180°.
CBSE Step-by-Step Marking Scheme
Straight angle identified
1 M
180° stated
1 M
Q22
Textbook Exercise • Quadrilateral Angle Sum
A quadrilateral has 4 angles. If three of its angles are 90°, 85°, and 95°, what is the measure of the fourth angle?
[3 Marks]
✅ Step-by-Step Solution & Working
Angle Sum of Quadrilateral:
• Sum of all 4 angles of a quadrilateral = 360°.
• Sum of given three angles = 90° + 85° + 95° = 270°.
• Fourth angle = 360° - 270° = 90°.
• Sum of all 4 angles of a quadrilateral = 360°.
• Sum of given three angles = 90° + 85° + 95° = 270°.
• Fourth angle = 360° - 270° = 90°.
CBSE Step-by-Step Marking Scheme
Total sum 360° stated
1 M
Sum of 3 angles: 270°
1 M
Fourth angle: 90°
1 M
Q23
Textbook Exercise • Pentagon Internal Angles
A regular pentagon has 5 equal sides. (a) How many angles does it have? (b) Are its internal angles acute, right, or obtuse?
[2 Marks]
✅ Step-by-Step Solution & Working
Pentagon Properties:
• (a) Number of angles: A pentagon has 5 angles.
• (b) Angle type: Each internal angle of a regular pentagon measures 108°, which is greater than 90°. Therefore, all its internal angles are Obtuse Angles.
• (a) Number of angles: A pentagon has 5 angles.
• (b) Angle type: Each internal angle of a regular pentagon measures 108°, which is greater than 90°. Therefore, all its internal angles are Obtuse Angles.
CBSE Step-by-Step Marking Scheme
5 angles stated
1 M
Obtuse angles (108°) identified
1 M
Q24
Textbook Exercise • Paper Folding Right Angle
Describe how you can fold a circular piece of paper to produce a perfect right angle (90°).
[2 Marks]
✅ Step-by-Step Solution & Working
Paper Folding Method:
1. Take a round piece of paper and fold it exactly in half to form a semicircle. The crease line represents a straight angle of 180°.
2. Fold the semicircle in half once again, matching the curved edges and straight corners perfectly.
3. Press the fold firmly. The corner formed at the centre point is exactly 1/4 of a full circle (360° ÷ 4), creating a perfect Right Angle of 90°.
1. Take a round piece of paper and fold it exactly in half to form a semicircle. The crease line represents a straight angle of 180°.
2. Fold the semicircle in half once again, matching the curved edges and straight corners perfectly.
3. Press the fold firmly. The corner formed at the centre point is exactly 1/4 of a full circle (360° ÷ 4), creating a perfect Right Angle of 90°.
CBSE Step-by-Step Marking Scheme
Step 1: Half fold (semicircle)
1 M
Step 2: Quarter fold producing 90° corner
1 M
🌟 NEP 2020 Competency-Based Case Study
NEP 2020 Competency Case: Shapes and Angles
A practical scenario involving Shapes and Angles in everyday life and community contexts.
Analytical Task: Analyze the quantitative relationships and state the conclusion.
Evaluation & Model Answer:
Apply the step-by-step formulas and concepts mastered in this chapter.
Rubric: 1M formula + 1M working + 1M answer