Question

In circle O, AD and BE are diameters. What is MAE?

Answer 1

132°

Explanation:

∠AOB = ∠EOD = 3x ( vertical angles )

∠AOB + ∠BOC = 90, that is

3x + 0.5x + 34 = 90

3.5x + 34 = 90 ( subtract 34 from both sides )

3.5x = 56 ( divide both sides by 3.5 )

x = 16

∠AOE + ∠EOD = 180 ( straight angle )

∠AOE + 3x = 180

∠AOE + (3 × 16) = 180

∠AOE + 48 = 180 ( subtract 48 from both sides )

∠AOE = 132°

Answer 2

The answer is 132°

Explanation:

It is given that

AD and BE are diameters

From the figure we get

<AOB = <EOD = 3x (Vertically opposite angles are equal)

and <AOC =90

3x + 0.5x + 34 = 90

x = 16

<EOD = 3x= 48

To Find <EOA

<EOA + <AOB =180 (Linear pair)

<EOA = 180 - 48 =132

Therefore measure of AE = 132

second option is the correct answer