what is the measure of angle efd? 37.5° 45° 47.5° 55°
what is the measure of angle efd? 37.5° 45° 47.5° 55°
Answer
Answer:
C. $47.5^{\circ}$
Explanation:
Step1: Recall inscribed - angle theorem
The measure of an inscribed angle is half the measure of its intercepted arc.
Step2: Identify the intercepted arc
The inscribed angle $\angle EFD$ intercepts arc $\overset{\frown}{ED}$, and the measure of arc $\overset{\frown}{ED}=95^{\circ}$.
Step3: Calculate the measure of $\angle EFD$
By the inscribed - angle theorem, $m\angle EFD=\frac{1}{2}m\overset{\frown}{ED}$. Substituting $m\overset{\frown}{ED} = 95^{\circ}$, we get $m\angle EFD=\frac{95^{\circ}}{2}=47.5^{\circ}$.