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In the diagram, PR is a diameter of the circle PQRS. PST ...

In the diagram, PR is a diameter of the circle PQRS. PST and QRT are straight lines. Find QRS

In the diagram, PR is a diameter of the circle PQRS. PST and QRT are straight lines. Find QRS

A.

20o

B.

25o

C.

30o

D.

35o

Correct answer is B

< PSR = \(\frac{1}{2}\)(180o) = 90o (angle substended by a semi-circle)

∴ < TSR = 90o

< SRT = 90o - 30o = 60o

< PRS = 90o - 35o = 55o

< PRQ = 180 - (60o + 55o) = 180 - 115o = 65o

< SQR = 35o(angles in the same segment)

< QSR + < SRQ + < SQR = 180o

< QSR + 120o + 35o = 180o

< QSR + 155 = 180o

< QSR = 180o - 155o

= 25o