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

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

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${}^{\circ }$