Worksheet on Basic Geometrical Ideas

Solved Questions on Basic Geometrical Ideas

1. What is the value of ∠EBD?

a) 65°
b) 75°
c) 105°
d) 115°

Answer: b) 75°

Explanation: In the given figure, ∠EBD is marked.

In triangle ABC, 

∠ABC + ∠BAC + ∠ACB = 180° (Sum of its three angles in a triangle is 180°)
⇒ ∠ABC + 60° + 45° = 180°
⇒ ∠ABC + 105° = 180°
⇒ ∠ABC = 180° − 105°
⇒ ∠ABC = 75°   

∠EBD = ∠ABC = 75° (Vertically Opposite Angle)

2. What is the value of x°?

a)
b)
c)
d)

Answer: c)

Explanation: (x + 30)° +  (x − 20)° +  2x° +  (x + 45)° +  (x − 5)° +  (x + 25)° = 360°

⇒ 7x° + 75° = 360°
⇒ 7x° = 360° − 75°
⇒ 7x° = 285°
⇒ x° = 285°/7

3. What is the length of OH if the length of AE is 9.39 cm?

a) 4.5 cm
b) 4.7 cm
c) 4.9 cm
d) 4.95 cm

Answer: b) 4.7 cm

Explanation: Length of AE (Diameter) = 9.39 cm

Length of OH (Radius)
= Diameter/2
= AE/2
= 9.39 cm/2
= 4.695 cm
= 4.70 cm (Round off)

4. What is the value of x if ∠ABC = 55°, ∠CAB = 32° and obtuse angle AED = 115°?

a) 22°
b) 26°
c) 28°
d) 30°

Answer: c) 28° 

Explanation: Given: ∠ABC = 55°, ∠CAB = 32° and ∠AED =115°

Exterior angle of a triangle is the sum of the measure of the two interior angles that are opposite to it. 

In △ABC, 

∠ACD = ∠ABC + ∠CAB
⇒ ∠ACD = 55° + 32°
⇒ ∠ACD = 87°

 In △CDE,

∠EDC + ∠ECD = ∠AED     (∠ACD and ∠ECD is the same angle)
⇒ x + 87° = 115° 
⇒ x = 115° − 87°
⇒ x = 28°

5. What is the diameter of the circular field if the circumference is 363 metres?

a) 52.25 m
b) 52.75 m
c) 57.25 m
d) 57.75 m

Answer: d) 57.75 m

Explanation: Circumference of the circle = 363 metres

⇒ 2 × ²²⁄₇ × r = 363 
⇒ r = 363 × ¹⁄₂ × ⁷⁄₂₂
⇒ r = 57.75 m