SSC CGL 2022 PYQ — Question 59

The correct answer is option 3 i.e. 69°

∠ROS = 42⁰

The sum of the angles of a triangle = 180⁰

Exterior angle = Sum of opposite interior angles.

Angle made by an arc at the center = 2 × Angle made by the same arc at any point on the circumference of the circle

Join RQ and RS.

According to the above point -

∠RQS = ∠ROS/2

∠RQS = 42/2 = 21⁰ .....(1

PQ is a diameter.

∠PRQ = 90⁰ [Angle in the semicircle = 90⁰]

In ΔRQT -

∠PRQ is an exterior angle.

∠PRQ = ∠RTQ + ∠TQR = 90⁰ = ∠RTQ + 21⁰ [∠TQR = ∠RQS = 21⁰]

∠RTQ = 90⁰ - 21⁰ = 69⁰

∠PTQ = 69⁰