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

Answer:

C. $160^{\circ}$

Explanation:

Step1: Recall the central - inscribed angle relationship

The measure of an inscribed angle is half the measure of the central angle that subtends the same arc.

Step2: Identify the inscribed and central angles

Inscribed angle $\angle B = 80^{\circ}$, and central angle $\angle COA$ subtends the same arc as $\angle B$.

Step3: Calculate the measure of $\angle COA$

Let $\theta$ be the measure of $\angle COA$. Since $\angle B=\frac{1}{2}\theta$, then $\theta = 2\times\angle B$. Substitute $\angle B = 80^{\circ}$ into the formula: $\theta=2\times80^{\circ}=160^{\circ}$.