Question

Find ∠AEC in the figure below.

Answer 1

Answer: C. 105

Explanation:

Adding BED and DEC for being adjacent angles we obtain:

`2y+x +-2y+3x = 180\\4x = 180\\x=45\\`

Substituting x in BEA

`BEA=2(45)-15=75`

Adding BEA and AEC for being adjacent angles we obtain:

`BEA+AEC=180\\AEC=180-BEA\\AEC=180-75\\AEC=105`

Answer 2

C. 105°

Explanation:

Angles BED and CED are supplementary, so ...

(2y +x) +(-2y +3x) = 180

4x = 180

2x = 90

Substituting this into the expression for angle AEB, we have ...

Angle AEB = (90 -15)° = 75°

Angle AEC is the supplement to that, so is ...

∠AEC = 180° -75° = 105° . . . . . matches choice C