Question

question 6 of 10 if the measure of ∠abc is 68°, what is the measure of ⁀ab? a. 136° b. 68° c. 34° d. 112°

Explanation:

Step1: Recall inscribed - angle theorem

The measure of an inscribed angle is half the measure of its intercepted arc.

Step2: Set up the equation

Let the measure of arc $\widehat{AB}$ be $x$. Given $\angle ABC = 68^{\circ}$, and $\angle ABC$ is an inscribed angle intercepting arc $\widehat{AB}$. So, $\angle ABC=\frac{1}{2}\text{measure of arc }\widehat{AB}$.

Step3: Solve for the arc measure

We have $68^{\circ}=\frac{1}{2}x$. Multiply both sides by 2: $x = 2\times68^{\circ}=136^{\circ}$.

Answer:

A. $136^{\circ}$