Question

$\text{The corresponding sides of two triangles}△ABC\text{and}△PQR\text{are in the ratio 4:23.}$$\text{If}\angle B={60}^{\circ }\text{and}\angle A={40}^{\circ },\text{find the}\text{measure of}\angle R.$

• A. ${80}^{\circ }$
• B. ${90}^{\circ }$
• C. ${100}^{\circ }$
• D. ${110}^{\circ }$

Answer 1

The correct option is A

${80}^{\circ }$

We know that if the corresponding sides of two triangles are in the same ratio, then the two triangles are similar.

Here, the corresponding sides are in the ratio 4:23.

$\Rightarrow$ $△ABC\sim △PQR$

$\text{In}△ABC$,

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

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

$\Rightarrow \angle C$ = ${180}^{\circ }$ - ${60}^{\circ }$ - ${40}^{\circ }$ = ${80}^{\circ }$

$\text{Since}△ABC\sim △PQR,\angle C=\angle R\text{(Corresponding angles of similar}\text{triangles are equal)}$

$\text{So,}\angle R={80}^{\circ }$