Worksheet on Understanding Elementary Shape

Solved Questions on Understanding Elementary Shape

1. In the given figure, AOB is a straight line. If ∠AOD = 69° and ∠BOC = 47°,   what is the value of ∠COD?

a) 44°
b) 54°
c) 64°
d) 74°

Answer: c) 64°

Explanation: ∠AOD + ∠COD + ∠BOC = 180° [Supplementary angles]
⇒ 69° + ∠COD + 47° = 180°
⇒ ∠COD + 116° = 180°
⇒ ∠COD = 180° − 116°
⇒ ∠COD = 64°

2. The sum of all the interior angles of a polygon is 2340°. How many sides does the polygon have?

a) 9
b) 11
c) 13
d) 15

Answer: d) 15

Explanation: Sum of interior angles in a polygon = 2340°

⇒ (n − 2) × 180° = 2340°
⇒ (n − 2) = 2340°/180°
⇒ n − 2 = 13
⇒ n = 13 + 2
⇒ n = 15

3. In the given figure, AOC is a straight line. If ∠AOE = 90°, ∠AOB = 52° and ∠COD = 27°. What is the measure of ∠EOD?

a) 33°
b) 43°
c) 53°
d) 63°

Answer: d) 63°

Explanation: ∠AOE + ∠COE = 180° [AOC is a straight line, Linear Pair]

⇒ 90° + ∠COE = 180°
⇒ ∠COE = 180° −  90°
⇒ ∠COE = 90°
∠EOD + ∠COD = ∠COE (Complementary Angles)
⇒ ∠EOD + 27° = 90°
⇒ ∠EOD = 90° – 27°
⇒ ∠EOD = 63°

4. What is the value of 1.5y?

a) 35°
b) 55°
c) 55°/3
d) 110°/3

Answer: b) 55°

Explanation: Figure shows the complete angle which is 360°.

⇒ y + 75° + 2y + 65° + 3y = 360°
⇒ 6y + 140° = 360°
⇒ 6y = 360° − 140°
⇒ 6y = 220°
⇒ y = 220°/6
⇒ y =  110°/3

The value of 1.5y is:

⇒ 1.5y =  1.5 × 110°/3 = 55°

5. For an angle z°, What is the value of z°/2 if its supplement is three times its complement?

a) 15 ½°
b) 22 ½°
c) 37 ½°
d) 45°

Answer: b) 22 ½°

Explanation: Supplement of an angle z° is three times its complement.

⇒ Supplement of an angle z° = 3 × Complement of an angle z°
⇒ 180° − z° = 3 × (90° − z°)
⇒ 180° − z° = 270° − 3z°
⇒ 3z° − z° = 270° − 180°
⇒ 2z° = 90°
⇒ z° = 90°/2
⇒ z° = 45°

The value of z°/2  = 45°/2 = 22 ½°