CPM Homework Help : GC Problem 10-7

In the diagram below, $\overline{AD}$ is a diameter of $⊙B$ .

Circle with points, A, C, and D, on the circle, and B, in the center. Line segments connect B to all 3 points on the circle. Single tick marks, on segments, A B, B D, and B C.

If $m∠A = 35°$ , what is $m∠CBD$ ?
Hint (a):
$∠A$ is the inscribed angle and $∠CBD$ is the central angle intercepting the same arc.
How are these angles related?
Answer (a):
$70°$
If $m∠CBD = 100°$ , what is $m∠A$ ?
Answer (b):
$50°$
If $m∠A = x$ , what is $m∠CBD$ ?
Hint (c):
Use the same method you used to solve part (a).