In △ABC, BD ⊥ AC at D. E is a point on BC such that ∠ BEA = x°. If ∠ EAC = 46° and ∠ EBD = 60°, then the value of x is :
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Correct answer: A
Explanation
The correct answer is option 1 i.e. 76°
BD ⊥ AC at D.
E is a point on BC such that ∠BEA = x0
∠EAC = 460
∠ EBD = 620
In ΔAOD -
∠AOD + ∠ADO + ∠DAO = 1800
∠AOD + 900 + 460 = 1800
∠AOD = 1800 - 1360
∠AOD = 440
∠AOD and ∠EOB are vertically opposite angles.
∠AOD = ∠EOB = 440
In ΔBOE -
∠BEO + ∠EOB + ∠OBE = 1800
x0 + 440 + 600 = 1800
x0 = 1800 - 1040
x0 = 760