Question

what is the measure of angle coa? 140° 150° 160° 170°

Explanation:

Step1: Recall the central - inscribed angle relationship

The measure of an inscribed angle is half the measure of the central angle subtended by the same arc. Angle $\angle B$ is an inscribed angle and $\angle COA$ is the central angle subtended by the same arc $\overset{\frown}{CA}$.

Step2: Apply the formula

If the measure of inscribed angle $\angle B = 80^{\circ}$, and let the measure of central angle $\angle COA=x$. According to the formula $\angle B=\frac{1}{2}\angle COA$, we have $x = 2\angle B$.

Step3: Calculate the value of $\angle COA$

Substitute $\angle B = 80^{\circ}$ into the formula $x = 2\angle B$, then $x=2\times80^{\circ}=160^{\circ}$.

Answer:

C. $160^{\circ}$