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?
image of a circle with center o, points m, n, p on the circumference, and point q outside the circle with tangents to m and p
m∠mnp
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Explanation:

Step1: Find reflex ∠MOP's supplement

The total degrees around a point is $360^\circ$. Subtract the given reflex angle to find the smaller central angle.
$$m\angle MOP_{\text{small}} = 360^\circ - 219^\circ = 141^\circ$$

Step2: Calculate inscribed ∠MNP

An inscribed angle is half the measure of its intercepted central angle.
$$m\angle MNP = \frac{1}{2} \times 141^\circ = 70.5^\circ$$

Answer:

70.5