Question

In this figure,
←→
B
E
and
←→
A
D
intersect at point C.

The measure of angle B-C-A is X plus 10 degrees and the measure of angle D-C-E is 4 times X minus 35 degrees.

What is the degree measure of
∠
B
C
A
?

A.
15
°

B.
25
°

C.
80
°

D.
170
°

Answer 1

Lines BE and AD cross, so ∠BCA and ∠DCE are vertical angles and therefore equal. Set x + 10 = 4x − 35.

Solve: 45 = 3x, so x = 15. Then ∠BCA = x + 10 = 15 + 10 = 25°.

Answer: B (25°).