Question

please koi help kar do mari please Q.25​

Answer 1

Step-by-step explanation:

(i) See first imae

Given :-

$\angle{POR} : \angle{ROQ} = 5 :7$

$Let \: \angle{POR } = 5x$

$and \: \angle{ROQ }= 7x$

Now,

$\angle{POR} + \angle{ROQ} = 180° \: (linear \: pair \: of \: angles)$

$5x + 7x = 180°$

$12x = 180°$

$x = \frac{180°}{12}$

$x = 15°$

$\angle{POR} =5x = 5 \times 15 =75°$

$\angle{ROQ} = 7x = 7 \times 15 = 105°$

Now,

$∠POS=∠ROQ=105° (Vertically \: opposite \: angles)$

$and ∠SOQ=∠POR=75°   (Vertically \: opposite \: angles)$

(ii) See second image

According to the figure,

∠EOB,∠BOD and ∠DOF are the angles on a straight line.

Where,

∠DOF = 50°

and ∠BOD = 90°

$thus \: ∠EOB+∠BOD+∠DOF=180° \: (linear \: pair \: of \: angles)$

$x + 90°+50°=180°$

$x + 140°=180°$

$x = 180°- 140°$

$x = 40°$

$\scriptsize{x°=y°(Vertically \: opposite \: angles \: are \: equal)}$

$y = 40°$

$\scriptsize{z° = \angle{DOF} \: ( Vertically \: opposite \: angles \: are \: equal)}$

$z = 50°$

$\scriptsize{v = ∠BOD° \: (Vertically \: opposite \: angles \: are \: equal)}$

$v = 90°$

Hence x = 40°, y = 40°, z = 50°, v = 90°

(iii) See third image

We know that the sum of all the angles in a straight line is 180°

$\scriptsize{∠BOC+∠COD+∠AOD=180° (linear \: pair \: of \: angles)}$

$\scriptsize(x+20)+x+(x+10)=180°$

$x+20+x+x+10=180°$

$3x+30=180°$

$3x=180° - 30$

$3x = 150°$

$x = \frac{150°}{3}$

$x = 50°$

$∠AOD=x+10°$

$=50°+10°$

$= 60°$

$∠BOC=x+20°$

$=50°+20°$

$= 70°$

$\scriptsize∴∠COD=50°,∠AOD=60°and \: ∠BOC =70°$

(iv) See forth image

We have two straight lines PQ and RS.

$And,∠ POT = 75°$

$\scriptsize{So,∠ POR + ∠ POT + ∠ TOS = 180°(Linear \: pair \: angles)}$

Now substitute the given values,

we get -

$4b + 75° + b = 180°$

$5b = 180° - 75°$

$5b = 105°$

$b = \frac{ 105°}{5}$

$b = 21°$

$And, ∠ POR = 4b$

$∠ POR = 4 \times 21$

$∠ POR = 84°$

$\scriptsize∠ SOQ =∠ POR   (vertically \: opposite \: angles)$

$\angle{SOQ} = 84°$

$\because \angle{SOQ} = a$

$\therefore \: \: a = 84°$

$∠ QOR = ∠ POS (vertically \: opposite \: angles)$

Substitute the values, we get-

$2c = 75° + 21°$

$2c = 96°$

$c = \frac{96}{2}$

$c = 48°$

$So,a = 84°, b = 21°, c = 48°$

I hope it is helpful