Question

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

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

Answer 1

The correct option is D

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

Givem, $△ABC\cong △XYZ$
It can be seen that $△ABC\cong △XYZ$ by the AAS congruence rule
With
$\angle C=\angle Z$ (given)
$\angle A=\angle X$
BC = YZ (given)
We know, the corresponding parts of congruent triangles are equal.

Hence, $\angle A=\angle X={30}^{\circ }$

In $△ABC$,
We have.
$\angle A$ + $\angle B$ + $\angle C$ = ${180}^{\circ }$
=> ${30}^{\circ }$ + $x$ + ${70}^{\circ }$ = ${180}^{\circ }$
$x$ = $({180}^{\circ }-{30}^{\circ }-{70}^{\circ })$ = 80${}^{\circ }$