Question

Given

m2 ABD is a straight angle.
m ABC = 8x - 41°
mZCBD = 9x + 17°
Find m2CBD:
А
B
D

Answer 1

∠CBD = 125°

Explanation:

The angle sum theorem tells you that ...

∠ABC +∠CBD = ∠ABD

8x -41° +9x +17° = 180° . . . . . . a "straight angle" has a measure of 180°

17x -24° = 180° . . . simpify

17x = 204° . . . . . . add 24°

x = 12° . . . . . . . . . . divide by 17

Now the measures of the angles can be found from their expressions.

∠ABC = 8(12) -41° = 55°

∠CBD = 9(12) +17° = 125°