In the figure, PQRS is a circle with ST||RQ. Find the value of x if...

Mathematics

JAMB 1999

In the figure, PQRS is a circle with ST||RQ. Find the value of x if PT = pS

A. 70^o
B. 55^o
C. 40^o
D. 35^o

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Correct Answer: Option B

Explanation

< PST = < RQT = x(corresponding angle)

< PST = < PTS = < PTS x (PS = PT0

< SRQ = < SPT = 180^o (sum of < on straight line)

< SPT = 180^o - 110^o = 70^o

in < SPT, < PST = PTS = < PSt = 180^o

2x + 70 = 180^o

2x = 180^o - 70^o = 110^o

x = \(\frac{110^o}{2}\) = 55^o

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