If $ riangle A B C \sim riangle P Q R$ with $\angle A=32^{\circ}$ and $\angle R=65^{\circ}$, then

Question

If $	riangle A B C \sim 	riangle P Q R$ with $\angle A=32^{\circ}$ and $\angle R=65^{\circ}$, then the measure of $\angle B$ is :\

Professor PC Thomas Classes · Answer

(c): Since, $	riangle A B C \sim 	riangle P Q R$\ $\Rightarrow \angle A=\angle P, \angle B=\angle Q$ and $\angle C=\angle R=65^{\circ}$\ Now, $\angle A+\angle B+\angle C=180^{\circ} \quad$ (Angle sum property)\ $\Rightarrow 32^{\circ}+\angle B+65^{\circ}=180^{\circ}$\ $\Rightarrow \quad \angle B=180^{\circ}-65^{\circ}-32^{\circ}=83^{\circ}$ \ Commonly made Mistake : Don't mix up similar triangles and congruent triangle, student might say, similar triangle have equal sides (which is false). They might assume congruent triangles, only have equal angle (which is false).