6. In the diagram shown, PQR is a straight line. |PQ| = |QS| = |QR| |∠QPS| = 25° (i) What is the measure of angle w? Give a reason for your answer. (ii) Calculate the measure of angle x. (iii) Calculate the measure of angle y.
P 7.
(i) Find the value of x as shown in the diagram. Justify your answer.
(ii) Find the value of y as shown in the diagram. Justify your answer.
y° x° 85° 150°
S w° y° 25° x° Q R
8. The shape ABCD shown is a parallelogram.
Find the measure of the angle x shown in the diagram. Justify all steps used to find your answer.
38° D
A 120° E 41° x C
B
9. Calculate the value of x shown in the diagram. Justify all steps taken to find your answer.
B 53° A D
10. In the diagram shown, O is the centre of the circle. (i) By what name is [BC] better known? (ii) Find the measure of ∠OAC. (iii) Find the measure of ∠AOB. Justify your answers in both (ii) and (iii).