Question

If $△ABC$ and $△PQR$ in the below figure are similar, find the missing length x and the measure of $\angle R$

• A. 20 cm,60°
• B. 20 cm,22 °
• C. 22 cm,20°
• D. 25 cm.100°

Answer 1

The correct option is C

22 cm,20°

Consider $△ABC$ Now, by the angle sum property of a triangle, $\angle C=180-(\angle A+\angle B)=180-(100+60)=20°$.

Given that $△ABC\sim △PQR$ , hence the corresponding angles are equal and the corresponding sides are in proportion.

Therefore, $\angle C=\angle R=20°$

SInce sides are in proportion , we have

$⟹\frac{AB}{PQ}=\frac{BC}{QR}$

$⟹\frac{13}{26}=\frac{11}{x}$

$⟹x=22cm$