Question

Find the measure of ∠AED.
A) 25°
B) 65°
C) 115°
D) 155°

Answer 1

D. 155° is correct

5x = 3x + 10
2x = 10
x = 5

5x = 25

180 - 25 = 155°

Answer 2

Option D. 155°

Explanation:

Two lines AC and BD are intersecting each other at point E.

Since ∠DEC = ∠AEB [ opposite angles ]

5x = 3x = 10

2x = 10

x = 5 ⇒ ∠DEC = ( 3×5 ) + 10 = 15 + 10 = 25°

Now we have to find ∠AED

Since ∠AED + ∠DEC = 180° [Supplementary angles]

∠AED + 25 = 180

∠AED = 180 - 25

∠AED = 155°

Option D. is the answer.