Question

question 3 of 5 type the correct answer in the box. use numerals instead of words. if necessary, use / for the fraction bars. the measure of ∠mop is 219° as shown. what is the measure of ∠mnp? m∠mnp =

Explanation:

Step1: Recall the inscribed - angle and central - angle relationship

The measure of an inscribed angle is half the measure of the intercepted arc's central angle. The central angle corresponding to the major arc $\overset{\frown}{MP}$ is $\angle MOP = 219^{\circ}$, and the central angle corresponding to the minor arc $\overset{\frown}{MP}$ is $360^{\circ}-219^{\circ}=141^{\circ}$. The inscribed angle $\angle MNP$ intercepts the minor arc $\overset{\frown}{MP}$.

Step2: Calculate the measure of $\angle MNP$

By the inscribed - angle theorem, $m\angle MNP=\frac{1}{2}$ (measure of the central angle of the intercepted arc). So $m\angle MNP=\frac{1}{2}(360 - 219)$.
$m\angle MNP=\frac{1}{2}\times141 = 70.5$.

Answer:

$70.5$