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In the diagram above, PQO is a diameter of the circle PQR. If < PSR = 145\(^{\circ}\) find x\(^{\circ}\)...


Question

In the diagram above, PQO is a diameter of the circle PQR. If < PSR = 145\(^{\circ}\) find x\(^{\circ}\)

Options

A) 35\(^{\circ}\)

B) 55\(^{\circ}\)

C) 25\(^{\circ}\)

D) 45\(^{\circ}\)

The correct answer is B.

Explanation:

Construction RQ

< PRQ = 90\(^{\circ}\)(amgle substended at the circumfernce of a circle by diameter). Also in figure PQRS

< PQS + PSQ = 180(supplementary angle)

< PQS = 180 - 145 = 35

In \(\bigtriangleup\)PRQ x = 180 - 935 = 90)

x = 55


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Dicussion (1)

  • Construction RQ

    < PRQ = 90\(^{\circ}\)(amgle substended at the circumfernce of a circle by diameter). Also in figure PQRS

    < PQS + PSQ = 180(supplementary angle)

    < PQS = 180 - 145 = 35

    In \(\bigtriangleup\)PRQ x = 180 - 935 = 90)

    x = 55

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