Question

In the given congruent triangles under ASA, find the value of x and y, ΔPQR $\cong$ ΔSTU.

Answer 1

Given: ΔPQR $\cong$ ΔSTU (By ASA rule)
∠Q = ∠T = ${60}^{\circ }$ (given)
QR = TU= 4 cm (given)
∠x = ${30}^{\circ }$ (C.P.C.T.)
Now in ΔSTU,
∠S + ∠T + ∠U = ${180}^{\circ }$(Angle sum property)
∠y + ${60}^{\circ }$+ ∠x = ${180}^{\circ }$
∠y + ${60}^{\circ }+30°={180}^{\circ }$
∠y + ${90}^{\circ }={180}^{\circ }$
∠y =${180}^{\circ }-{90}^{\circ }={90}^{\circ }$
Hence, $\angle x={30}^{\circ }$ and $\angle y={90}^{\circ }$