ANGLE IN SEMICIRCLE WORKSHEET

Problem 1 :

P, Q and R are points on the circumference of a circle, center O. PR is the diameter of the circle and ST is a tangent to the circle at the point R.

∠QRS = 58

a)  Work out the size of angle QRP.

b)  Work out the size of the angle QPR.

Solution

Problem 2 :

Work out the size of each angle marked with a letter. Give reasons for your answers.

Solution

Problem 3 :

In the circle given below, U is the point of ST such that RUT is right angle.

find 

a) ∠URT    b)  ∠ROT    c)  ∠ORU      d)  ∠ORT

Solution

Problem 4 :

Solution

Problem 5 :

Work out the size of each angle marked with a letter. Give reasons for your answers.

Solution

Problem 6 :

In the given figure O is the center of the circle and SP is a tangent. If ∠SRT = 65, find the values of x, y and and z.

Solution

Problem 7 :

Work out the size of each angle marked with a letter. Give reasons for your answers.

Solution