In the diagram, PO and OR are radii, |PQ| = |QR| and reflex < PQR...

Mathematics

WAEC 2011

In the diagram, PO and OR are radii, |PQ| = |QR| and reflex < PQR is 240^o. Calculate the value x

A. 60^o
B. 55^o
C. 50^o
D. 45^o

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Correct Answer: Option A

Explanation

< Q = \(\frac{240}{2}\) (angle at centre twice that at the circumference)

< Q = 120^o

Also < POR = 360 - 240

= 120^o

( < s at centre) since /PQ/ = /QR/, < x = < R

Byt < x + < R + O + Q = 360 (sum of interior < s of quadrilateral)

x + R + 120 = 360^o

x + R = 360 - 240 = 120; Since x = R

x + x = 120

2x = 120

Since x = R

x + x = 120

2x = 120

x = \(\frac{120}{2}\)

= 60^o

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