Question

A circle is drawn with center O and points P, Q, R, S, and T falling upon it. All points are joined by line segments such that PS is a diameter, ∠QRS is obtuse, and ∠QTR is acute. Classify ∠PTS.

A. Straight angle
B. Obtuse angle
C. Right angle
D. Acute angle

Answer 1

Angle ∠PTS is a right angle since PS is a diameter, and angles subtended by a diameter in a circle are always right angles according to the Inscribed Angle Theorem.

Step-by-step explanation:

To classify the angle ∠PTS, we need to consider the properties of a circle and the information provided about the angles ∠QRS and ∠QTR. Given that PS is a diameter, any angle that is subtended by a diameter in a circle is a right angle due to the Inscribed Angle Theorem. Therefore, ∠PTS is a right angle.

Even though ∠QRS is given as obtuse and ∠QTR is acute, these angles do not directly impact the classification of ∠PTS because ∠PTS is uniquely determined by the fact that PS is a diameter. Therefore, ∠PTS does not depend on the obtuseness or acuteness of the other angles mentioned.