Question

select the correct answer.
points a, b, and c are located on a circle, and chords exist between all three points. if the measure of ∠bac is 88°, what is the measure of ( overset{\frown}{bc} )?
a. 88°
b. 92°
c. 176°
d. 184°

Explanation:

Step1: Recall Inscribed Angle Theorem

The inscribed angle theorem states that an inscribed angle is half the measure of its intercepted arc. So, if $\angle BAC$ is an inscribed angle intercepting arc $BC$, then $m\angle BAC=\frac{1}{2}m\overset{\frown}{BC}$.

Step2: Solve for Arc $BC$ Measure

Given $m\angle BAC = 88^\circ$, we can solve for $m\overset{\frown}{BC}$ by rearranging the formula: $m\overset{\frown}{BC}=2\times m\angle BAC$. Substituting the given angle measure, we get $m\overset{\frown}{BC}=2\times88^\circ = 176^\circ$.

Answer:

C. $176^\circ$