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

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

Answer Details

PQRS is a cyclic quad
^P = 180 - 110 (opp ∠s of a cyclic quad)
^P = 70
In ΔPTS, ^S = ^T (base ∠s of Isc Δ)
∴^T = (180-70) / 2
= 110/2
= 55${}^{\circ }$
But ^T x(corr ∠)
∴x =55