line ef is tangent to circle g at point a. if the measure of ∠cae is 95°, what is the measure of…
line ef is tangent to circle g at point a. if the measure of ∠cae is 95°, what is the measure of (overset{\frown}{cba})? 90° 95° 190° 195°
Answer
Answer:
B. $95^{\circ}$
Explanation:
Step1: Recall tangent - chord angle theorem
The measure of an inscribed angle is equal to the measure of the intercepted arc's central angle divided by 2. Also, the measure of an angle formed by a tangent and a chord is equal to the measure of the inscribed angle subtended by the same arc.
Step2: Identify the relevant arcs and angles
$\angle CAE$ is an angle formed by tangent $EF$ and chord $AC$. $\overset{\frown}{CBA}$ is the arc intercepted by $\angle CAE$. According to the tangent - chord angle relationship, the measure of the angle formed by the tangent and the chord is equal to the measure of the intercepted arc. So, if $m\angle CAE = 95^{\circ}$, then $m\overset{\frown}{CBA}=95^{\circ}$.