If the measure of ∠ABD is 112°, what are the measures of ∠ABC and ∠CBD?
(2 points)
∠ABC=
°
and ∠CBD=
°
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If the measure of ∠ABD is 112°, we can use the fact that the sum of the angles in a triangle is 180° to find the measures of ∠ABC and ∠CBD.
∠ABC + ∠ABD + ∠CBD = 180°
We are given that ∠ABD = 112°, so we can substitute this into the equation:
∠ABC + 112° + ∠CBD = 180°
Now we can solve for ∠ABC and ∠CBD:
∠ABC + ∠CBD = 180° - 112°
∠ABC + ∠CBD = 68°
There are infinite solutions to this equation since the measure of ∠ABC and ∠CBD can vary as long as their sum is 68°. Therefore, we cannot determine the exact measures of ∠ABC and ∠CBD with the given information.