Question

find the measure of the arc. mef = ?°

Explanation:

Step1: Recall circle - angle property

The measure of a central angle is equal to the measure of the arc it intercepts.

Step2: Identify the central angle for arc EF

The central angle for arc $\overset{\frown}{EF}$ is the angle $\angle EOF$. In a circle, the sum of central - angles around a point is $360^{\circ}$. Given one of the central angles is $146^{\circ}$ and another is a right - angle ($90^{\circ}$).

Step3: Calculate the measure of $\angle EOF$

We know that $m\angle EOF+146^{\circ}+90^{\circ}=360^{\circ}$. Then $m\angle EOF = 360^{\circ}-(146^{\circ}+90^{\circ})$. First, calculate the sum inside the parentheses: $146^{\circ}+90^{\circ}=236^{\circ}$. Then $m\angle EOF=360^{\circ}-236^{\circ}=124^{\circ}$. Since the measure of an arc is equal to the measure of its central angle, $m\overset{\frown}{EF}=124^{\circ}$.

Answer:

$124$