Question

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

Explanation:

Step1: Recall the tangent - secant angle relationship

The measure of an angle formed by a tangent and a secant is half the measure of the intercepted arc. Here, $\angle CAE$ is an angle formed by tangent $EF$ and secant $AC$. Let the measure of arc $\overset{\frown}{CBA}$ be $x$.
The formula is $\angle CAE=\frac{1}{2}\text{ measure of arc }\overset{\frown}{CBA}$.

Step2: Solve for the measure of arc $\overset{\frown}{CBA}$

Given $\angle CAE = 95^{\circ}$, we can rewrite the formula as $95^{\circ}=\frac{1}{2}x$.
To find $x$, we multiply both sides of the equation by 2: $x = 2\times95^{\circ}=190^{\circ}$.

Answer:

$190^{\circ}$