Question

For what value of $x$ (in degrees) will $△ABC\cong △XYZ$ ?

• A. 80

Answer 1

The correct option is A 80
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 $△ABC$,
$\angle CAB+\angle ABC+\angle BCA={180}^{\circ }$
$\Rightarrow {30}^{\circ }+x+{70}^{\circ }={180}^{\circ }$
$x=({180}^{\circ }-{30}^{\circ }-{70}^{\circ })={80}^{\circ }$