Question

question 2 of 5
type the correct answer in the box. use numerals instead of words. if necessary, use / for the fraction bar(s).
the measure of ∠mop is 219° as shown. what is the measure of ∠mnp?
m∠mnp = □°

Explanation:

Step1: Find the measure of the central angle corresponding to the arc \( MNP \)

The full - circle is \( 360^{\circ} \). Given \( \angle MOP=219^{\circ} \), the central angle \( \angle MNP \) subtends an arc. The measure of the arc that is not part of \( \angle MOP \) is \( 360^{\circ}-\angle MOP \). So, the central angle for the arc \( MNP \) (let's call it \( \angle MONP_{central} \)) is \( 360 - 219=141^{\circ} \).

Step2: Use the inscribed - angle theorem

The inscribed - angle theorem states that the measure of an inscribed angle \( \angle MNP \) is half the measure of the central angle that subtends the same arc. If the central angle \( \angle MONP_{central}=141^{\circ} \), then the inscribed angle \( \angle MNP=\frac{1}{2}\times\angle MONP_{central} \).

Answer:

\( 70.5 \)