### Home > CCG > Chapter Ch10 > Lesson 10.1.4 > Problem10-43

10-43.

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

1. $m∠QSO$

$\overarc{QO} + \overarc{OS} = \overarc{QS}$

$\overarc{OS} = 80º$ and $\overarc{QS} = 180º$

$\overarc{QO} + 80º = 180º$

$\overarc{QO} = 100º$

An intercepted arc is twice its inscribed angle.

$m∠QSO = 50º$

1. $m∠QPO$

An intercepted arc is twice its inscribed angle.

$50º$

1. $m∠ONS$

$67º$

1. $m\overarc{ P S }$

An intercepted arc is twice its inscribed angle.

$126º$

1. $m\overarc{ P Q }$

$54º$

1. $m∠PQN$

$63º$