Question

In circle p below, ∠opm = 136° and line segments on and mn are tangents to the circle. what is the measure of ∠onm? what is the measure of ∠n? a. 56° b. 44° c. 74° d. 90°

Answer 1

The angle ∠onm is half of the central angle ∠opm (68°), and the angle ∠n is always 90° when a tangent meets a radius at the point of contact. Thus, the correct answer is option a. 56°

Step-by-step explanation:

In a circle, the angle formed by a tangent and a chord drawn from the point of contact is equal to half the angle subtended by the chord at the center. Therefore, ∠onm is half of ∠opm, which is (136°/2) = 68°.

Additionally, the angle between a tangent and a radius drawn at the point of contact is always 90°. Hence, ∠n is 90°.

Therefore, the measure of ∠onm is 68°, and the measure of ∠n is 90°, making option a. 56° the correct answer.

Thus, the correct answer is option a. 56°