Question

Line EF is tangent to circle G at point A. If the measure of Angle C A E is 95°, what is the measure of Arc C B A? 90° 95° 190° 195°.

Answer 1

Step-by-step explanation:

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Answer 2

Given:

EF is the tangent to the circle G at a point A.

Also given angle $CAE=95$°

To find the measure of the arc $CBA$

The alternate segment theorem (also known as the tangent-chord theorem) states that in any circle, the angle between a chord and a tangent through one of the endpoints of the chord is equal to the angle in the alternate segment.

An angle formed by a chord and a tangent that intersect on a circle is half the measure of the intercepted arc.

Given angle $CAE=(\frac{1}{2})\times angle CBA$

Angle $CBA=2\times$ angle $CAE$

Angle $CBA=2\times95$°

Angle $CBA=190$°

Line EF is tangent to circle G at point A. If the measure of Angle $CAE$ is $95$°, what is the measure of Arc $CBA?$

Summary:

If the line EF is tangent to circle G at point A. If the measure of Angle $CAE$ is $95$°, then the measure of Arc $CBA$ is $190$°