In the figure given below, PQ is the diameter of the circle with center O. if ∠QOR = 100° then the measure of ∠PSR is:
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 40°.
The angle made by an arc at the center is two times the angle made by the same arc at the circumference of the circle.
According to the given diagram,
∠QOR + ∠POR = 180°
⇒ ∠POR = 180° - 100°
⇒∠POR = 80°
Now, ∠POR is the angle at the center and ∠PSR is the angle at the circumference by arc PR,
⇒ ∠POR = 2 × ∠PSR
⇒ ∠PSR = 80°/2
⇒ ∠PSR = 40°