Question

If $△ABC\sim △PQR$ and $\angle B=\angle R={60}^{\circ }$, then 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: $△ABC\sim △PQR$
$\angle B=\angle R={60}^{\circ }$

Since $△ABC\sim △PQR$,
$\angle A=\angle P$
$\angle B=\angle Q$
$\angle C=\angle R$

$\Rightarrow$ $\angle Q=\angle B={60}^{\circ }$
and $\angle C=\angle R={60}^{\circ }$

Now, $\angle A={180}^{\circ }-\angle B-\angle C$
(Since sum of interior angles of a triangle is ${180}^{\circ }$)

$\Rightarrow$ $\angle A={180}^{\circ }-\angle B-\angle C$

$\Rightarrow$ $\angle A={180}^{\circ }-{60}^{\circ }-{60}^{\circ }$

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

$\therefore \angle RPQ=\angle A={60}^{\circ }$