Question

the measure of one and one of the angle forming a linear pair is less than the other angle by 100 find the measure of both angle​

Answer 1

$\mathfrak{\large{\underline{\underline{Answer :-}}}}$

The angles are 140° and 40°

$\mathfrak{\large{\underline{\underline{Explanation:-}}}}$

Given :

Measure of one angle = less than other Angle by 100

The angles are Linear Pairs

To Find :

The Measures of both the angles

Solution :

Consider -

• One Angle as x
• Second angle as x - 100

Linear Pairs are the adjacent angles which sum up and make 180°. They can be said as pair of adjacent Supplementary Angles.

★ x + (x - 100) = 180°

$\longrightarrow$ x + (x - 100) = 180

$\longrightarrow$ x + x - 100 = 180

$\longrightarrow$ 2x - 100 = 180

$\longrightarrow$ 2x = 180 + 100

$\longrightarrow$ 2x = 280

$\longrightarrow$ x = 280/2

$\longrightarrow$ x = 140

One angle is 140°.

$\rule{300}{1.5}$

★ Value of (x - 100)

$\longrightarrow$ 140 - 100

$\longrightarrow$ 40

Second angle is 40°.

$\therefore$ The angles are 140° and 40°.

$\rule{300}{1.5}$

$\mathfrak{\large{\underline{\underline{Verification :-}}}}$

Add the angles and check if they sum up 180° or not.

$\longrightarrow$ 140 + 40

$\longrightarrow$ 180

$\therefore$ The angles are 140° and 40°.

Answer 2

Question: The measure of one and one of the angle forming a linear pair is less than the other angle by 100. Find the measure of both angle.

Answer : 140° and 40° .

Solution : Let one of the angle be x° .

A/Q

the difference between the two angles is 100 .

So, other angle = x-100.

Given that the angles make up a linear pair

So, angle 1+ angle 2 =180° (linear pair)

x° + (x-100)° =180°

x°+x° -100° =180°

2x° =180°+100°

2x° =280°

x° =280°/2

x=140°

So, measure of first angle = 140° .

Second angle =x-100

=140°-100

=40°

So, the two angles are respectively 140° and 40° .