Question

If $△ABC$ and $△PQR$ are similar triangles such that $\angle A={32}^{\circ }$ and $\angle R={65}^{\circ }$ then $\angle B$ is

• A. ${83}^{\circ }$
• B. ${42}^{\circ }$
• C. ${65}^{\circ }$
• D. ${97}^{\circ }$

Answer 1

The correct option is A ${83}^{\circ }$

Since triangle ABC anD PQR are similar

$\therefore \angle A=\angle P,\angle B=\angle Qand\angle C=\angle R={65}^{\circ }$

In $△ABC$

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

${32}^{\circ }+\angle B+65={180}^{\circ }$

$\angle B={180}^{\circ }-{97}^{\circ }$

$\angle B={83}^{\circ }$