Question

line ef is tangent to circle g at point a. if the measure of ∠cae is 95°, what is the measure of cba? 90° 95° 190° 195°

Explanation:

Step1: Recall tangent - radius property

A tangent to a circle is perpendicular to the radius at the point of tangency. So, $\angle EAG = 90^{\circ}$.

Step2: Use angle - addition property

We know that $\angle CAE=95^{\circ}$ and $\angle EAG = 90^{\circ}$. Also, $\angle CAG=\angle CAE+\angle EAG$.
\[

$$\begin{align*} \angle CAG&=95^{\circ}+ 90^{\circ}\\ &=185^{\circ} \end{align*}$$

\]
The measure of an arc is equal to the measure of its central - angle. The measure of arc $\overparen{CBA}$ is the measure of the central angle $\angle CAG$.

Answer:

$185^{\circ}$