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

Assessment: JAMB UTME - Mathematics - 1999 Subject: General Mathematics

Question 1 Report

70

^{\circ}

55

^{\circ}

40

^{\circ}

35

^{\circ}

Answer Details

< PST = < RQT = x(corresponding angle)

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

< SRQ = < SPT = 180 $^{\circ}$ (sum of < on straight line)

< SPT = 180 $^{\circ}$ - 110 $^{\circ}$ = 70 $^{\circ}$

in < SPT, < PST = PTS = < PSt = 180 $^{\circ}$

2x + 70 = 180 $^{\circ}$

2x = 180 $^{\circ}$ - 70 $^{\circ}$ = 110 $^{\circ}$

x = $\frac{110^{o}}{2}$ = 55 $^{\circ}$

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