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# In the diagram, PO and OR are radii, |PQ| = |QR| and reflex <PQR is 240o. Cal...

### Question

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

A) 60o

B) 55o

C) 50o

D) 45o

### Explanation:

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

< Q = 120o

Also < POR = 360 - 240

= 120o

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

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

x + R + 120 = 360o

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

x + x = 120

2x = 120

Since x = R

x + x = 120

2x = 120

x = $$\frac{120}{2}$$

= 60o

## Dicussion (1)

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

< Q = 120o

Also < POR = 360 - 240

= 120o

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

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

x + R + 120 = 360o

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

x + x = 120

2x = 120

Since x = R

x + x = 120

2x = 120

x = $$\frac{120}{2}$$

= 60o