If the measure of ∠ABD is 112°, what are the measures of ∠ABC and ∠CBD? (2 points) ∠ABC= ° and ∠CBD= °
(3x+7)
(2x+5)
answer choices
(abc) 20, 45, 67, 80
cbd 40, 45, 92, 82
To find the measures of ∠ABC and ∠CBD, we can set up an equation using the fact that the sum of the angles in a triangle is 180°.
∠ABD = ∠ABC + ∠CBD
112° = ∠ABC + ∠CBD
We are given that ∠ABD = 112°. By substituting this value into the equation, we get:
112° = ∠ABC + ∠CBD
Since ∠ABD is supplementary to both ∠ABC and ∠CBD, we can set up the following equations:
∠ABC = 180° - 112°
∠CBD = 180° - 112°
Simplifying, we get:
∠ABC = 68°
∠CBD = 68°
Therefore, the measures of ∠ABC and ∠CBD are both 68°.