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 - arc relationship

The measure of an inscribed angle formed by a tangent and a chord is half the measure of the intercepted arc. Here, $\angle CAE$ is an angle formed by tangent $EF$ and chord $AC$, and $\overset{\frown}{CBA}$ is the intercepted arc.

Step2: Apply the formula

We know that the measure of the angle formed by a tangent and a chord is half the measure of the intercepted arc. So, if $\angle CAE = 95^{\circ}$, then the measure of $\overset{\frown}{CBA}=2\times\angle CAE$.
$m\overset{\frown}{CBA}=2\times95^{\circ}=190^{\circ}$

Answer:

C. $190^{\circ}$