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}\\)?
options: 190°, 195°, 95°, 90°

Explanation:

Step1: Use tangent-secant angle theorem

The measure of ∠CAE (tangent-secant angle) equals half the measure of its intercepted arc (arc CBA). So, $\text{arc } CBA = 2 \times \angle CAE$.

Step2: Calculate the arc measure

Substitute $\angle CAE = 95^\circ$: $\text{arc } CBA = 2 \times 95^\circ = 190^\circ$.

Answer:

A. 190°