Question

The corresponding sides of 2 similar triangles $△ABC$ and $△PQR$ are in the ratio 4:23. $\angle R$ is___________
Given that $\angle B$=${60}^{\circ }$ and $\angle A$= ${40}^{\circ }$.

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

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

So, $\angle C$ = ${180}^{\circ }$ -$\angle A$ - $\angle B$.

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

Since $△ABC$ ~ $△PQR$, $\angle C$= $\angle R$.

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