1) B
2)
A = 97°
B = 72°
Reason: opposite angles in a cyclic quadrilateral add up to 180°
3) 30°
4) 107°
Reason 1: the angle at the top left corner is 73° because the angle subtended by an arc at the centre is twice the angle subtended at the circumference.
Reason 2: opposite angles in a cyclic quadrilateral add up to 180°
5)
a) 75°
b) 105°
2)
A = 97°
B = 72°
Reason: opposite angles in a cyclic quadrilateral add up to 180°
3) 30°
4) 107°
Reason 1: the angle at the top left corner is 73° because the angle subtended by an arc at the centre is twice the angle subtended at the circumference.
Reason 2: opposite angles in a cyclic quadrilateral add up to 180°
5)
a) 75°
b) 105°
Working
Questions
You may use a calculator for the following questions. All of the diagram in the questions are not drawn to scale.
1) Which one of the two circles below contains a cyclic quadrilateral?
You may use a calculator for the following questions. All of the diagram in the questions are not drawn to scale.
1) Which one of the two circles below contains a cyclic quadrilateral?
2) What is the size of angle A and B? Give a reason for your answer.
3) What is the value of x?
4) What is the size of angle y? Clearly show with reasons how you obtained your answer.
Hint: Remember the previous circle theorems.
Hint: Remember the previous circle theorems.
5) Angles A and B are in the ratio of 5:7.
a) What is the size of angle A?
b) What is the size of angle B?
b) What is the size of angle B?