Question

Line ef is tangent to circle g at point a. If the measure of is 95°, what is the measure of ? 90° 95° 190° 195°.

Answer 1

The question as stated includes a possible typo or missing information, making it challenging to determine the measure of the missing angle. However, the angle between a tangent and radius of a circle at the point of tangency is always 90°.

Step-by-step explanation:

The measure of the angle formed by a tangent line to a circle and a radius at the point of tangency is 90°. This is because a tangent line is always perpendicular to the radius at the point where it touches the circle. Since the measure of ℓ ef is given as 95°, which doesn't correspond to this scenario, there seems to be confusion or a typo in the student's question. Without additional information or clarification, it is impossible to correctly determine the measure of the missing angle.

If the question meant to inquire about the angle between the tangent and radius at point A, then the answer would be 90°, as it is a fact that at the point of tangency, the tangent to a circle is perpendicular to the radius. However, if this is not the asked question, additional context is required to provide an accurate answer.

Answer 2

Applying the Inscribed Angle Theorem, the measure of arc CBA in the circle is calculated as: c. 190°.

What is the inscribed angle theorem?

The Inscribed Angle Theorem states that an angle formed by two chords in a circle is half the measure of the central angle subtending the same arc that the angle spans. This implies that if the inscribed angle measures 30 degrees, then the subtended arc will measure 60 degrees.

Given the image below, we have:

Inscribed angle = 95°

Subtended arc is arc CBA = 2(95)

Measure of arc CBA = 190° (option C).

Complete Question:

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

a. 90°

b. 95°

c. 190°

d. 195°