Question

Find the measure of angle AOE in the diagram below.
Help will be appreciated!

Answer 1

i believe the answer is c) 120

Answer 2

We choose D

Explanation:

Given that:

• ∠BOA = (3x -28) degrees
• ∠COD = (66 -x) degrees
• ∠BOC = 90 degrees

As we know that ∠BOA + ∠COD + ∠BOC= 180 degrees because AD is a straight line, so we have:

(3x -28) + (66-x) +90 = 180

<=> 2x = 52

<=> x = 26 degrees.

=> ∠BOA = 3*26 - 28 = 50 degrees

As we can see that, ∠BOA = ∠DOE (The properties of two straight lines intersect)

<=> ∠DOE = 50 degrees

Once again, the AD is a straight line, so we have:

∠DOE + ∠AOE = 180

<=> ∠AOE = 180 - ∠DOE

<=> ∠AOE = 180 - 50 = 130 degrees

We choose D