Question

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

Explanation:

Step1: Use the inscribed - angle theorem

The inscribed - angle theorem states that the measure of an inscribed angle $\angle B$ is half of the measure of the central angle $\angle COA$ that subtends the same arc $\overset{\frown}{CA}$. So, if the inscribed angle $\angle B = 80^{\circ}$, and let the central angle $\angle COA=x$. Then, according to the formula $\angle B=\frac{1}{2}\angle COA$.

Step2: Solve for the central angle

We have the equation $80^{\circ}=\frac{1}{2}x$. Multiply both sides of the equation by 2: $x = 2\times80^{\circ}=160^{\circ}$.

Answer:

$160^{\circ}$