Question

Find ∠AEC in the figure below.

Answer 1

Answer: C. 105

Step-by-step 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

Answer:

  C. 105°

Step-by-step 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