In △ABC, BD ⊥ AC atD.E is a point on BC such that ∠BEA = x°. If ∠EAC = 62° and ∠EBD = 60°, then the value of X is:
Show answer & explanation
Correct answer: D
Explanation
The correct answer is Option 4 i.e 92°.
Given:
BD ⊥ AC at D.
E is a point on BC such that ∠BEA = x°
∠EAC = 62°
∠EBD = 60°
In ΔAOD,
∠AOD + ∠ADO + ∠DAO = 180°
⇒ ∠AOD + 90° + 62° = 180°
⇒ ∠AOD =180° - 152°
⇒ ∠AOD = 28°
∠AOD and ∠EOB are vertically opposite angles,
∠AOD = ∠EOB = 28°
Ιn ΔΒΟΕ,
∠BEO + ∠EOB + ∠OBE = 180°
x° + 28° + 60° = 180°
⇒ x° = 180° - 88°
⇒ x° = 92°
The value of x is 92°