# 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

1)  ∠QRP = 32, ∠QPR = 58

2)  b = 66

3)  ∠STR = 53, ∠TRU = 37, ROT = 74

4) g = 35

5)  g = 62, h = 28

6)  x = 25, y = 50 and z = 40

7)  e = 108, d = 36, f = 54

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