Question

For what value of $x$ will $△ABC\cong △XYZ$ ?

• A. $x={50}^{\circ }$
• B. $x={30}^{\circ }$
• C. $x={70}^{\circ }$
• D. $x={80}^{\circ }$

Answer 1

The correct option is D

$x={80}^{\circ }$

Given,
$△ABC\cong △XYZ$
and
$\angle BCA=\angle YZX$ ... (given)
$BC=YZ$ ... (given)

Since $△ABC\cong △XYZ$,
We know that, the corresponding parts of congruent triangles are equal.
So, $\angle CAB=\angle ZXY={30}^{\circ }$

In $△ABC$,
$\angle CAB$ + $\angle ABC$ + $\angle BCA$ = ${180}^{\circ }$
=> ${30}^{\circ }$ + $x$ + ${70}^{\circ }$ = ${180}^{\circ }$
$x$ = $({180}^{\circ }-{30}^{\circ }-{70}^{\circ })$ = ${80}^{\circ }$