Question

TP is a tangent to a circle TRQ with center O. If ∠TPO = 28° and ∠ORQ = 15°, find ∠RQT and ∠QTO.

A. ∠RQT = 57°, ∠QTO = 28°
B. ∠RQT = 28°, ∠QTO = 57°
C. ∠RQT = 43°, ∠QTO = 15°
D. ∠RQT = 15°, ∠QTO = 43°

Answer 1

To find ∠RQT and ∠QTO, use the properties of tangents and circles. ∠RQT = 75° and ∠QTO = 62°.

Step-by-step explanation:

To find ∠RQT and ∠QTO, we need to use the properties of tangents and circles. Since TP is a tangent to the circle at point T, we know that ∠TPO is 90° (tangent is perpendicular to the radius at the point of tangency). Also, since TRQ is a triangle and the sum of its angles is 180°, we can find ∠RQT by subtracting the given angles from 180°: ∠RQT = 180° - ∠TRQ - ∠RTQ = 180° - 15° - 90° = 75°.

Similarly, we can find ∠QTO by subtracting the given angles from 180°: ∠QTO = 180° - ∠TPO - ∠TOP = 180° - 28° - 90° = 62°.

The answer is

∠RQT = 75°

and

∠QTO = 62°

.