Question

n this figure, the measure of
∠
A
E
D
is 152°.

The rays A-E, B-E, C-E, and D-E starts from point E. The angle A-E-B measures X degrees, angle B-E-C measures 2-X degrees, angle C-E-D measures X minus 16 degrees.

What is the degree measure of
∠
C
E
D
?

A.
26°

B.
38°

C.
42°

D.
84°

Answer 1

Interpret the given: ∠AEB = x, ∠BEC = 2x, ∠CED = x − 16, and these three adjacent angles sum to ∠AED = 152°.

So x + 2x + (x − 16) = 152
⇒ 4x − 16 = 152
⇒ 4x = 168
⇒ x = 42.

Thus ∠CED = x − 16 = 42 − 16 = 26°.

Answer: A. 26°.