Question

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

Explanation:

Step1: Use the inscribed - angle theorem

The inscribed - angle theorem states that the measure of an inscribed angle $\angle CBA$ is half the measure of the central angle $\angle COA$ that subtends the same arc $\overset{\frown}{CA}$.
Let $\angle CBA = 80^{\circ}$, and $\angle COA$ be the central angle. Then $\angle CBA=\frac{1}{2}\angle COA$.

Step2: Solve for $\angle COA$

From the formula $\angle COA = 2\angle CBA$.
Substitute $\angle CBA = 80^{\circ}$ into the formula: $\angle COA=2\times80^{\circ}$.

Answer:

$160^{\circ}$