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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.

Options

A) 60o

B) 55o

C) 50o

D) 45o

The correct answer is A.

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


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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

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