Question

Given that $△PQR\cong △STU.$ under ASA congruence rule, find the value of x and y.

Answer 1

$\text{Given:}△PQR\cong △STU\text{( By ASA rule )}$

$\angle Q=\angle T={60}^{\circ }\text{(given)}$

$Q{R}^{-}=T{U}^{-}=4\text{cm (given)}$

$\angle x={30}^{\circ }(\text{for ASA rule)}$

$\text{Now in}△STU,$

$\angle S+\angle T+\angle U={180}^{\circ }(\text{Angle sum property)}$

$\angle y+{60}^{\circ }+\angle x={180}^{\circ }$

$\angle y+{60}^{\circ }+{30}^{\circ }={180}^{\circ }$

$\angle y+{90}^{\circ }={180}^{\circ }$

$\angle y={180}^{\circ }-{90}^{\circ }={90}^{\circ }$

$\text{Hence,}x={30}^{\circ }\text{and}y={90}^{\circ }$