In the figure, PQRS is a circle. If chords QR and RS are equal, calculate the value of x.

In the figure, PQRS is a circle. If chords QR and RS are equal, calculate the value of x.

Answer Details

SRT is a straight line, where QRT = 120

SRQ = 180${}^{\circ }$ - 120${}^{\circ }$ = 60${}^{\circ }$ - (angle on a straight line)

also angle QRS = 180${}^{\circ }$ - 100${}^{\circ }$ (angle on a straight line) . In angles where QR = SR and angle SRQ = 60${}^{\circ }$

x = 100 - 60 = 40${}^{\circ }$