Question

It is given that $△ABC\sim △PQR$ and $\angle B=\angle R={60}^{\circ }$. Find $\angle RPQ$.

• A. ${120}^{\circ }$
• B. ${60}^{\circ }$
• C. ${30}^{\circ }$
• D. ${90}^{\circ }$

Answer 1

The correct option is B ${60}^{\circ }$

Given:
$△ABC\sim △PQR$
$\angle B={60}^{\circ }$
$\angle R={60}^{\circ }$

$△ABC\sim △PQR$
So, their corresponding angles are equal. So, we get:
$\angle Q=\angle B={60}^{\circ }$
$\angle C=\angle R={60}^{\circ }$
$\angle A=\angle P$

Sum of the angles in a triangle is ${180}^{\circ }$.
$\angle P+\angle Q+\angle R={180}^{\circ }$
$\angle P+{60}^{\circ }+{60}^{\circ }={180}^{\circ }$
$\angle P={60}^{\circ }$

$\Rightarrow \angle RPQ={60}^{\circ }$