Question

guys plz ans this
its ok if u ans any one​

Answer 1

1. x=40 degree

2.x=95 degree

Answer 2

Solution :

• in fig. (i)

☞︎︎︎ Finding angle a :

• here

$\\ \large \sf \mapsto \: 105\degree + \angle \: a = 180 \degree \\ \: \: \: \: ( \: linear \: \: pair \: )$

Angles along a straight line = 180°

$\\ \large \tt \implies \angle \: a = 180 \degree - 105 \degree \\ \\ \large \sf \therefore \: \underline{ \underline{ \angle \: a = 75 \degree}}$

☞︎︎︎ Finding angle b :

$\\ \large \sf \mapsto \: 45\degree + \angle \: b = 180 \degree \\ \: \: \: \: ( \: linear \: \: pair \: )$

$\large \tt \implies \angle \: b= 180 \degree - 45 \degree \\ \\ \large \sf \therefore \: \underline{ \underline{ \angle \: b= 135 \degree}}$

☞︎︎︎ Finding angle x :

• let angle with x be = y

here,

$\\ \large \sf \mapsto \: \angle \: x + \angle \: y = 180 \degree \\ \: \: \: \: ( \: linear \: \: pair \: )$

$\large \leadsto \rm \angle \: y = \angle \: a \: \\ (alternate \: \: interior \: \: angles \: ) \\ \\ \large \sf \therefore \angle \: y = 75 \degree$

$\large \implies \sf \angle \: x + 75 \degree = 180 \degree \\ \\ \large \sf \implies \angle \: x = 180 \degree - 75 \degree \\ \\ \large \sf \therefore \: \underline{ \underline{ \angle \: x = 105 \degree}}$

_________________________________________

• in fig. (ii)

☞︎︎︎ let non given angle be = y

$\\ \large \sf \mapsto \: \angle \: y + 55 \degree + 60 \degree = 180 \degree \\ \: \: \: linear \: \: pair \\ \\ \large \sf \implies \angle \: y + 105 \degree = 180 \degree \\ \\ \large \sf \implies \angle \: y = 180 \degree - 105 \degree \\ \\ \large \sf \therefore \: \underline{ \underline{ \angle \: y= 75 \degree}}$

Construction :

Draw a straight line joining x with x

• Take angels of lower triangle :

(with angle y ) = x¹ and x²

• Angels of upper triangle= x³ and x⁴

here,

$\\ \large \sf \: joining : \: {x}^{1} + {x}^{2} + {x}^{3} + {x}^{4}$

• gives the value of 2x = ( x + x )

☞︎︎︎ Finding x¹ and x² :

$\\ \large \rm \underline{ \star \: angle \: \: sum \: \: property}$

$\large \tt \implies \: {x}^{} + {x}^{} + 75 \degree = 180 \degree \\ \\ \large \tt \implies \: 2x = 180 \degree - 75 \degree \\ \\ \large \tt \implies \: x = \frac{105}{2} \\ \\ \large \tt \star \: \: x = 52.5 \degree$

Angle Sum Property for upper triangle:

$\\ \large \tt \implies \: x + x + 105 \degree = 180 \degree \\ \\ \large \tt \implies \: 2x = 180 \degree - 105 \degree \\ \\ \large \tt \implies \: x = \frac{75}{2} \\ \\ \large \sf \: \star \: \: x = 32.5$

True Value of x :

$\\ \large \sf \: \leadsto \: {x}^{1} + {x}^{2}$

• x¹ = 52.5

• x² = 32.5

$\\ \large \sf \: \implies \: 52.5 + 32.5 = x \\ \\ \large \star \: \underline{ \underline{ \sf \: x = 85 \degree}}$