Question

In the figure, PQRS in an isosceles trapezium. Find x and y.

Answer 1

$\because PQRS$ is an isoceles trapezium in which SP = RQ and SR || PQ

$\therefore \angle P+\angle S={180}^{\circ }$ (Sum of co-interior angles)

$3x+2x={180}^{\circ }\Rightarrow 5x={180}^{\circ }$

$\Rightarrow x=\frac{{180}^{\circ }}{5}={36}^{\circ }$

But $\angle P=\angle Q$

(Base angles of isosceles trapezium)

$y=2x=2\times {36}^{\circ }={72}^{\circ }$

$\therefore y={72}^{\circ }$

Hence $x={36}^{\circ },y={72}^{\circ }$