Question

line ef is tangent to circle g at point a. if the measure of ∠cae is 95°, what is the measure of (overarc{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 half the measure of its intercepted arc. So $m\angle CAE = \frac{1}{2}m\overset{\frown}{CBA}$.

Step2: Solve for $m\overset{\frown}{CBA}$

Rearrange the formula to isolate the arc measure: $m\overset{\frown}{CBA} = 2 \times m\angle CAE$
Substitute $m\angle CAE = 95^\circ$:
$m\overset{\frown}{CBA} = 2 \times 95^\circ = 190^\circ$

Answer:

190° (Option C)