Question

For what value of $x$ will $△ABC$ be congruent to $△XYZ$ ?

• A. $x={50}^{\circ }$
• B. $x={60}^{\circ }$
• C. $x={40}^{\circ }$
• D. $x={30}^{\circ }$

Answer 1

The correct option is C $x={40}^{\circ }$

Given, $\angle A=40°$.
In $△$ABC and $△$XYZ,
$\angle B=\angle Y=90°$
$AB=XY=8\text{cm}$
For $△$ABC to be congruent to $△$XYZ,
$\angle A=\angle X=40°$.
$\text{Then,}△$ABC $\cong$ $△$XYZ $\cdots$ (by ASA criterion)
$\Rightarrow x={40}^{\circ }$