Each of the pairs of opposite angles made by two intersecting lines is called a vertical angle. The measure of ∠AOE is 132°. The correct option is B.
Each of the pairs of opposite angles made by two intersecting lines is called a vertical angle.
In circle O, AD and BE are diameters. Also, the measure of ∠EOD and ∠AOB will be equal because the two angles are vertically opposite angles. Therefore,
∠EOD = ∠AOB = 3x
As it is given that the measure of ∠AOC is 90°. Therefore, we can write,
∠AOC = ∠AOB + ∠BOC
90 = 3x + 0.5x + 34
56 = 3.5x
x = 16
Now, the measure of ∠EOD will be,
∠EOD = 3x
∠EOD = 3(16°)
∠EOD = 48°
Further, we can write,
∠AOD = ∠AOE + ∠EOD
180° = ∠AOE + 48°
∠AOE = 132°
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