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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