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

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

WAEC 2015

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.

A. 73^o
B. 67^o
C. 57^o
D. 37^o

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Correct Answer: Option 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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