Question

In the given figure $\angle BCA$ = $\angle RPQ$ = ${25}^{\circ }$, then find $\angle PQR$.

• A. ${35}^{\circ }$
• B. ${55}^{\circ }$
• C. ${45}^{\circ }$
• D. ${25}^{\circ }$

Answer 1

The correct option is C

${45}^{\circ }$

${45}^{\circ }$

The 2 triangles are congruent by SAS criterion of congruency i.e. $\delta ABC$ is congruent to $\delta QRP$
In the congruent triangles, the remaining angles are equivalent to each other.

Thus, $\angle PQR$ corresponds to $\angle CAB$

$\angle CAB$ = ${45}^{\circ }$ [Since it is on a straight line with the other two angles summing upto 135 degrees]

$\therefore$ $\angle PQR$ = ${45}^{\circ }$