Question

Observe the given figure and find the value of $\angle R$.

• A. ${40}^{\circ }$
• B. ${50}^{\circ }$
• C. ${60}^{\circ }$
• D. ${80}^{\circ }$

Answer 1

The correct option is A ${40}^{\circ }$

In $△ABC$ and $△PQR$,

$\frac{AB}{PQ}=\frac{3.8}{7.6}=\frac{1}{2}$

$\frac{BC}{QR}=\frac{6}{12}=\frac{1}{2}$

$\frac{CA}{PR}=\frac{3\sqrt{3}}{6\sqrt{3}}=\frac{1}{2}$

Therefore, $\frac{AB}{PQ}=\frac{BC}{QR}=\frac{CA}{PR}$

So, $△ABC$ is similar to $△PQR$.

$\angle C=\angle R$ (Corresponding angles of similar triangles)

Also, $\angle C={180}^{\circ }-\angle A-\angle B$ (Angle sum property)

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

$\angle C={40}^{\circ }$

Therefore, $\angle R={40}^{\circ }$