Question

For the given congruent triangles $PQR$ and $STU$ under ASA criterion, find the value of $x$ and $y$.

• A. $x={30}^{\circ },y={90}^{\circ }$
• B. $x={90}^{\circ },y={30}^{\circ }$
• C. $x={60}^{\circ },y={60}^{\circ }$
• D. $x={20}^{\circ },y={100}^{\circ }$

Answer 1

The correct option is A $x={30}^{\circ },y={90}^{\circ }$

Given: $\Delta PQR\cong \Delta STU$ (By ASA rule)
$\angle Q=\angle T={60}^{\circ }$ (given)
$QR=TU=4\text{cm}$ (given)
$\angle x={30}^{\circ }$ (for ASA rule)
Now in $\Delta STU$,
$\angle S+\angle T+\angle U={180}^{\circ }$ (Angle sum property)
$\angle y+{60}^{\circ }+\angle x={180}^{\circ }$
$\angle y+{60}^{\circ }+{30}^{\circ }={180}^{\circ }$
$\angle y+{90}^{\circ }={180}^{\circ }$
$\angle y={180}^{\circ }-{90}^{\circ }={90}^{\circ }$
Hence, $x={30}^{\circ }$ and $y={90}^{\circ }$