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dybincka [34]
4 years ago
8

Find ∠AEC in the figure below.

Mathematics
2 answers:
Ksivusya [100]4 years ago
7 0

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

Anastaziya [24]4 years ago
6 0

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

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