CPM Homework Help : CCG Problem 10-43

If $\overline{QS}$ is a diameter and $\overline{PO}$ is a chord of the circle at right, find the measure of the geometric parts listed below.

Circle, with points, in order, s, o, q, p, line segments from, q, to, s, from, q, to, p, from, p, to o, from, o, to s, with chord, q, s, and chord, p, o, intersecting at point, n, angle, n, o, s, labeled, 63 degrees, arc, s, o, labeled, 80 degrees.

$m∠QSO$
Hint (a):
$\overarc{QO} + \overarc{OS} = \overarc{QS}$
Step (a):
$\overarc{OS}=80°$ and $\overarc{QS}=180°$
$\overarc{QO}+80°=180°$
$\overarc{QO}=100°$
More Help (a):
An intercepted arc is twice its inscribed angle.
Answer (a):
$m∠QSO=50°$

$m∠QPO$
Hint (b):
An intercepted arc is twice its inscribed angle.
Answer (b):
$50°$

$m∠ONS$
Answer (c):
$67°$

$m\overarc{ P S }$
Hint (d):
An intercepted arc is twice its inscribed angle.
Answer (d):
$126°$

$m\overarc{ P Q }$
Answer (e):
$54°$

$m∠PQN$
Answer (f):
$63°$