Question

$\Delta ABC\sim \Delta PQR$. If $\angle B$ of $\Delta ABC$ and $\angle R$ of $\Delta PQR$ are ${60}^{\circ }$, then $\angle$ RPQ =

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

Answer 1

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

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

Here, $\angle B=\angle Qand\angle C=\angle R$
[$\because$ $△ABC$ $\sim$ $△PQR$, corresponding angles will be equal ]

$\Rightarrow$ $\angle B=\angle Q={60}^{\circ }$,
$\angle C=\angle R={60}^{\circ }$ and
$\angle A=\angle P$
As sum of the angles in a triangle is ${180}^{\circ },\angle A=\angle P={60}^{\circ }$.
$\Rightarrow \angle RPQ={60}^{\circ }$