If the measure of ∠ABD is 112°, what are the measures of ∠ABC and ∠CBD? (2 points) ∠ABC= ° and ∠CBD= °
(3x+7)
(2x+5)
We are given that ∠ABD is 112°. This angle is an exterior angle of a triangle, so it is equal to the sum of the measures of the two opposite interior angles, ∠ABC and ∠CBD.
Therefore, we can set up the equation: ∠ABD = ∠ABC + ∠CBD
Substituting the values given in the options:
112° = (3x+7) + (2x+5)
Now, we can solve for x:
112° = 3x + 7 + 2x + 5
Combine like terms:
112° = 5x + 12
Subtract 12 from both sides:
100° = 5x
Divide both sides by 5:
20° = x
Now that we have found x, we can substitute it back into the options to find the measures of the other angles:
∠ABC = 3x + 7
∠ABC = 3(20) + 7
∠ABC = 60 + 7
∠ABC = 67°
∠CBD = 2x + 5
∠CBD = 2(20) + 5
∠CBD = 40 + 5
∠CBD = 45°
Therefore, ∠ABC = 67° and ∠CBD = 45°.