Points P, Q, R, S and lie in this order on a circle with centre O. If chord TS is parallel to diameter PR and ∠RQT = 58° then find the measure (in degrees) of ∠RTS.

32

In this figure, \(\angle\)PQR = \({90}^\circ\)

and \(\angle\)PQT = \({90}^\circ\) - \({58}^\circ\) = \({32}^\circ\)

Now we know angle formed on same chord are equal.

Therefore, \(\angle\)PQT = \(\angle\)PRT

And \(\angle\)PRT = \(\angle\)RTS (Alternate angle)

\(\angle\)RTS = \({32}^\circ\).