# ANGLE SUBTENDED AT THE CENTER OF THE CIRCLE BY AN ARC WORKSHEET

In each of the following figures, O is the center of the circle. Calculate the values of x and justify your answer.

Problem 1 :

Solution

Problem 2 :

Solution

Problem 3 :

Solution

Problem 4 :

Solution

Problem 5 :

Solution

Problem 6 :

Solution

Problem 7 :

P, Q and R are points on the circumference of a circle, center O. Angle PRQ = 64, SP and SQ are tangents to the circle at the points P and Q respectively. Work out the size of angle.

i) ∠PSQ     ii)  ∠POS        iii)  ∠QSO

Solution

## Answer Key

1) x = 68

2) x = 73˚

3) x = 98˚

4)  x = 124˚

5)  x = 50˚

6)  x = 55˚

7)  i)  ∠PSQ = 52   ii)  ∠POS = 26   iii)  ∠QSO = 64

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