Question

lines PQ & RS intersect Each Other at O. if angle POR : ANGLE ROQ= 5 : 7 FIND all angles a, b, c and d

Answer 1

☺️hey mate! here's your answer!☺️

let x be the ratio between the angles such that,

5:7 = 5x and 7x

then,

by Linear pair axiom,

5x + 7x = 180°

=> 12x = 180°

=> x = 180/12

=> x = 15° ..answer

so,

angle 5x = 5 × 15 = 75°

angle 7x = 7 × 15 = 105°

then,

angle POR = QOS ( VERTICALLY OPPOSITE ANGLES)

angle QOR = SOP ( VERTICALLY OPPOSITE ANGLES)

HOPE IT WAS HELPFUL ✌️

Answer 2

$\huge{\pink{\underline{\ulcorner{\star\: Solution\: \star}\urcorner}}}$

$\red{\underline{Given\: \colon}}$

PQ & RS are intersect each other at point O.

$\frac{\angle{POR}}{\angle{ROQ}}= \frac{c}{d}=\frac{5}{7}$

$\red{\underline{Solution\: \colon}}$

$\frac{\angle{POR}}{\angle{ROQ}}= \frac{\angle{c}}{\angle{d}}=\frac{5x}{7x}$

Let ,

$\angle{c} =5x \\\\ \angle{d}=7x$

Using the linear pair property we get,

$\therefore\:\angle{c}+\angle{d} =180\degree \\\\ 5x\: + \: 7x = 180\degree\\\\ 12 x = 180\degree\\\\ x = \frac{\cancel{180}}{\cancel{12}} \\\\ x = 15\degree$

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$\therefore\:\angle{c} =5x = 5\times 15 \\\\ \implies \angle{c} = 75\degree \\\\\therefore \angle{d} =7x = 7\times 15 \\\\ \implies \angle{d} = 105\degree$

By vertically opposite angle property

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$\therefore\:\angle{c} = \angle{a} = 75\degree$

$\therefore\:\angle{b} = \angle{d} = 105\degree$

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$\red{\underline{Answer}}$

$\bold{\boxed{\angle{a} = \angle{c} = 75\degree}}$

$\bold{\boxed{\angle{b} = \angle{d} = 105\degree}}$

Thanks