The diagram is a circle with centre P. PRST are points on the circle. Find the value of < PRS

The diagram is a circle with centre P. PRST are points on the circle. Find the value of < PRS

A.

144o

B.

72o

C.

40o

D.

36o

Correct answer is A

Reflex < POS = 2x (angle at centre is twice that at circumference)

reflex < POS + < POS = 350o(angles at a point)

i.e. 2x + 8x = 360o

10x = 360o

x = \(\frac{360}{10}\)

= 36o

< PRS = \(\frac{1}{2}\)

< POS(< at centre twice that circumference)

= \(\frac{1}{2}\) x 8x = 4x

4 x 36o

< PRS = 144