Question

segment mp is a diameter of circle o
which equation can be used to find ( moverarc{mn} )?
( moverarc{mn} + 150 = 180 )
( moverarc{mn} - 150 = 180 )
( moverarc{mn} + 150 = 360 )
( moverarc{mn} - 150 = 360 )

Explanation:

Step1: Recall diameter property

A diameter divides the circle into two semicircles, so the arc \( \overset{\frown}{MP} \) is a semicircle with measure \( 180^\circ \).

Step2: Analyze arc addition

The arc \( \overset{\frown}{MP} \) is composed of \( \overset{\frown}{MN} \) and the \( 150^\circ \) arc. So, \( m\overset{\frown}{MN} + 150^\circ = 180^\circ \) (since \( m\overset{\frown}{MP}=180^\circ \)).

Answer:

\( m\overset{\frown}{MN} + 150 = 180 \) (the first option)