Explanation:
To find the measures of angles CBD and ABC in triangle ABC where segment BD bisects angle ABC, you can use the angle bisector theorem. According to the theorem, if a segment bisects an angle in a triangle, it divides the opposite side in such a way that the ratio of the two line segments is equal to the ratio of the two adjacent sides.
In this case:
m/ABD = m/ACD (since BD bisects angle ABC)
Now, let's denote the measure of angle ABD as (8x + 35) degrees. Then, the measure of angle ACD is also (8x + 35) degrees.
Now, to find m/CBD and m/ABC:
m/CBD = 180 - m/ABD - m/ACD (because the angles in a triangle add up to 180 degrees)
m/CBD = 180 - (8x + 35) - (8x + 35)
m/CBD = 180 - 16x - 70
Now, let's simplify:
m/CBD = 110 - 16x
Next, for m/ABC:
m/ABC = m/ABD + m/CBD (because angle ABC is the sum of angles ABD and CBD)
m/ABC = (8x + 35) + (110 - 16x)
Now, simplify:
m/ABC = 8x + 35 + 110 - 16x
m/ABC = 144 - 8x
So, the measures of the angles are as follows:
m/ABD = (8x + 35) degrees
m/CBD = 110 - 16x degrees
m/ABC = 144 - 8x degrees
None of the answer choices provided matches these calculations. It seems there might be an error in the options given, or there could be a mistake in the problem statement.