Question

in circle n with $m\angle mnp = 50^\circ$, find the $m\angle mqp$.

Explanation:

Step1: Relate central angle to arc

The measure of central angle $\angle MNP$ equals the measure of its intercepted arc $\overset{\frown}{MP}$.
$m\overset{\frown}{MP} = m\angle MNP = 50^\circ$

Step2: Use inscribed angle theorem

An inscribed angle is half its intercepted arc. $\angle MQP$ intercepts $\overset{\frown}{MP}$.
$m\angle MQP = \frac{1}{2}m\overset{\frown}{MP}$

Step3: Calculate the inscribed angle

Substitute the arc measure into the formula.
$m\angle MQP = \frac{1}{2} \times 50^\circ = 25^\circ$

Answer:

$25^\circ$