Question

$\huge\fbox\colour{lime}{Question}$


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

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Answer 1

refer to the attachment for the explanation

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°