Question : Two similar triangles are given i.e. $\triangle$LMN ~ $\triangle$PQR, with measurement of angle and side as $\angle$ L = 40°, $\angle$ N = 80°, LM = 6 cm, LN = 8 cm and PQ = 7.5 cm. Find the value of $\angle$ Q and side PR, respectively.
Option 1: 60° and 20 cm
Option 2: 50° and 6.5 cm
Option 3: 40° and 10 cm
Option 4: 60° and 10 cm
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Correct Answer: 60° and 10 cm
Solution : As $\triangle LMN$ and $\triangle PQR$ are similar ⇒ $\angle L = \angle P=40°$ and $\angle N = \angle R=80°$ We know, the sum of angles of a triangle = 180° ⇒ $\angle P + \angle Q + \angle R=180°$ ⇒ $40°+\angle Q + 80° = 180°$ ⇒ $\angle Q = 60°$ Also, the ratio of their sides will be equal ⇒ $\frac{LM}{LN}=\frac{PQ}{PR}$ ⇒ $\frac{6}{8}=\frac{7.5}{PR}$ ⇒ $PR=\frac{8\times7.5}{6}=10$ cm Hence, the correct answer is 60° and 10 cm.
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