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The diagram is a circle with centre P. PRST are points on...

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.

144^o

B.

72^o

C.

40^o

D.

36^o

View answer & explanation

Correct answer is A

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

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

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

10x = 360^o

x = $\frac{360}{10}$

= 36^o

< PRS = $\frac{1}{2}$

< POS(< at centre twice that circumference)

= $\frac{1}{2}$ x 8x = 4x

4 x 36^o

< PRS = 144

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