CPM Homework Help : GC Problem 10-17

In $⊙A$ at right, $\overline{CF}$ , is a diameter and $m∠C = 64°$ . Find:

A circle, with center point A, has 5 points clockwise about the circle, B, F, E, D, C, Line segments connect the following pairs of points: from, C to F, through, A, from, A, to B, from, B, to C, from, B, to D, from, B, to E, from, D to F, from, F to e.

$m \angle D$
Hint (a):
How is $∠D$ related to $∠C$ ?
Answer (a):
$∠D$ and $∠C$ are both inscribed angles with the same intercepted arc. So, $∠D ≅ ∠C = 64^{\large\circ}$ .

$m\overarc{ B F }$
Hint (b):
Use the same method you used for part (a).
Answer (b):
The measure of the intercepted arc is twice the measure of the inscribed angle. So, the measure is $128^{\large\circ}$ .

$m∠E$
Answer (c):
$64^{\large\circ}$

$m\overarc{ C B F }$

$m∠BAF$

$m∠BAC$