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  • The angle P in the following figure is <div class='qna-

The angle P in the following figure is

Option: 1

50°


Option: 2

60°


Option: 3

70°


Option: 4

None of these


Answers (1)

best_answer

\text { In } \triangle A B C \text { and } \triangle Q R P, \text { we have }

\\\frac{A B}{Q R}=\frac{3.6}{7.2}=\frac{1}{2}, \\\frac{B C}{R P}=\frac{6}{12}=\frac{1}{2} \\\text { and } \frac{C A}{P Q}=\frac{3 \sqrt{3}}{6 \sqrt{3}}=\frac{1}{2}

\text { Thus, } \frac{A B}{Q R}=\frac{B C}{R P}=\frac{C A}{P Q} \text { and so }

\triangle A B C \sim \triangle Q R P \quad[\text { by SSS-similarity }]

\therefore \quad \angle C=\angle P \quad[\text { corresponding angles of similar triangles }]\begin{array}{l} \text { But, } \angle C=180^{\circ}-(\angle A+\angle B)=180^{\circ}-\left(70^{\circ}+60^{\circ}\right)=50^{\circ} \\ \therefore \quad \angle P=50^{\circ} \end{array}

Posted by

Ritika Kankaria

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