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In the diagram, O is the centre, \(\bar{RT}\) is a diameter, < PQT = 33\(^o\)...


Question

In the diagram, O is the centre, \(\bar{RT}\) is a diameter, < PQT = 33\(^o\) and <TOS = 76\(^o\). Using the diagram, calculate the value of angle PTR.

Options

A) 73o

B) 67o

C) 57o

D) 37o

The correct answer is C.

Explanation:

In the diagram given, < PRT = 3\(^o\) (Change in same segment)

< TPR = 90\(^o\) (angle in a semicircle)

Hence, < PTR = 180\(^o\) - (90 + 33)\(^o\)

= 180\(^o\) - 123\(^o\)

= 57\(^o\)


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Dicussion (1)

  • In the diagram given, < PRT = 3\(^o\) (Change in same segment)

    < TPR = 90\(^o\) (angle in a semicircle)

    Hence, < PTR = 180\(^o\) - (90 + 33)\(^o\)

    = 180\(^o\) - 123\(^o\)

    = 57\(^o\)

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