Question

line ef is tangent to circle g at point a. if the measure of ∠cae is 95°, what is the measure of (widehat{cba})? ( \bigcirc 90^circ ) ( \bigcirc 95^circ ) ( \bigcirc 190^circ ) ( \bigcirc 195^circ )

Explanation:

Step1: Recall tangent-chord angle theorem

The measure of an angle formed by a tangent and a chord is equal to half the measure of its intercepted arc.

Step2: Relate angle to intercepted arc

$\angle CAE$ intercepts arc $\widehat{CBA}$, so $\angle CAE = \frac{1}{2}m\widehat{CBA}$

Step3: Solve for arc measure

Rearrange to solve for $m\widehat{CBA}$: $m\widehat{CBA} = 2 \times \angle CAE$
Substitute $\angle CAE = 95^\circ$: $m\widehat{CBA} = 2 \times 95^\circ = 190^\circ$

Answer:

190°