Question

In the given figure ; AOC-is a straight line. If angle AOB = 50°, angle AOE = 90° and angle COD = 25° ; find the measure of:

(i) angle BOC
(ii) angle EOD
(iii) obtuse angle BOD
(iv) reflex angle BOD
(v) reflex angle COE.

Answer 1

(i) ∠AOB + ∠BOC = 180° (Linear pairs of angle)

⇒ 50° +∠BOC = 180°

⇒ ∠BOC = 180° – 50° = 130°

⇒ ∠BOC = 130°

(ii) ∠EOD + ∠COD = 90° (∵AOE = 90°)

⇒ ∠EOD + 25° = 90°

⇒ ∠EOD + 25° = 90°

⇒ ∠EOD = 90° – 25°

⇒ ∠EOD = 65°

(iii) ∠BOD = ∠BOC + COD

= 130° + 25° = 155°

(iv) Reflex ∠BOD = 360° – ∠BOD

= 360°- 155° = 205°

(v) Reflex ∠COE = 360° – ∠COE

= 360° (∠COD + ∠EOD)

= 360° – (25° + 65°)

= 360° – 90° = 270°