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In the diagram, O is the centre of the circle. If SOQ is a diameter...

Mathematics
JAMB 1994

In the diagram, O is the centre of the circle. If SOQ is a diameter and < PRS is 38o, what is the value of < PSQ
  • A. 148o
  • B. 104o
  • C. 80o
  • D. 52o
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Correct Answer: Option D
Explanation
< SRP = < SQP = 38o (angle in the same segment of a circle are equal)

But < SPQ = 90o (angle in a semicircle)

also < PSQ + < SQP + < SPQ = 180o (angles in a triangle = 180o)

< PSQ + 38o + 90o = 190o

< PSQ = 128o = 180o

PSQ = 180o - 128o

PSQ = 52o

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