Question

what is the measure of arc ef in circle h?
○ 41°
○ 50°
○ 114°
○ 173°

Explanation:

Step1: Recall inscribed angle theorem

The measure of an inscribed angle is half the measure of its intercepted arc. So, $\text{Arc } DG = 2\times m\angle DEF$

Step2: Calculate arc DG

$m\angle DEF = 123^\circ$, so $\text{Arc } DG = 2\times123^\circ = 246^\circ$

Step3: Find total remaining arc

A full circle is $360^\circ$. Subtract arc DG: $360^\circ - 246^\circ = 114^\circ$

Step4: Subtract arc DE to get arc EF

We know $\text{Arc } DE = 73^\circ$, so $\text{Arc } EF = 114^\circ - 73^\circ = 41^\circ$

Answer:

A. $41^\circ$