Question

substitution method :
The Larger Of Two Supplementary angles exceeds the smaller by 18 degree. find them​

Answer 1

Answer:

Let, x and y be the two supplementary angles where angle y>x

x + y = 180. ...(1)

and, y - x = 18. .....(2)

By substitution method

from (1). y = 180 - x

putting above value to equation (2)

180-x-x = 18

or, 2x = 162

or, x = 81. and. y = 99

Hence, two angles are 99 and 81 respectively.

Answer 2

$\huge\underbrace\mathfrak\color{lime}{ †\: Question:–}$

The larger of two supplementary angle exceeds the smaller by 18 degree .Find them

$\huge\underbrace\mathfrak\color{lime}{ †\: Answer:–}$

Let larger angle be = x

Smaller angle be = y

According to the problem ;

Larger angle + smaller angle = 180°

$~~~~~~~~~~\longrightarrow$$\bold{x° + y° = 180°}$ ----------(1)

Larger angle = smaller angle + 18° (the smaller by 18 degree)

$~~~~~~~~~~\longrightarrow$$\bold{x° = y° + 18°}$ ----------(2)

Substitute eq(2) in eq(1)

$~~~~~~~~~~\longrightarrow$$\bold{y + 18° + y = 180°}$

$~~~~~~~~~~\longrightarrow$$\bold{2y + 18° = 180°}$

$~~~~~~~~~~\longrightarrow$$\bold{2y = 180° - 18°}$

$~~~~~~~~~~\longrightarrow$$\bold{2y = 162}$

$~~~~~~~~~~\longrightarrow$$\bold{y = \frac{162°}{2°}}$

$~~~~~~~~~~\longrightarrow$$\bold{y = 81°}$

So ;

Smaller angle is = 81°

$~~~~~~~~~~\longrightarrow$$\bold{x = y + 18°}$

$~~~~~~~~~~\longrightarrow$$\bold{x = 81° + 18°}$

$~~~~~~~~~~\longrightarrow$$\bold{x = 99°}$

Larger Number is = 99°