Question

If the supplement of an angle is 4 times of its compliment, find the angle.

Answer 1

Given:

• The supplement or an angle is given as 4 times of it's compliment.

To Find :

• We are asked to find the angle.

Let us take the angle as x

Now, the supplement of that angle would be 180 - x

And the complement of that angle would be 90 - x

According to the question,

The supplement is given as 4 times of it's complement.

Hence,

Supplement = 4 ( complement )

Writing this as an equation, we get,

$\implies{ \sf{180 - x = 4(90 - x)}}$

$\implies{ \sf{180 - x = 360 - 4x}}$

$\implies{ \sf{3x = 180}}$

$\implies{ \sf{x = \frac{180}{3} }}$

$\implies{ \boxed{ \sf{ \red{x = 60}}}}$

___________________

The angle is 60.

The supplement of it is 180 - 60 = 120.

And the complement of that angle is 90 - 60 = 30.

_________________________

Answer 2

Answer:

Step-by-step explanation:

Given:

The supplement or an angle is given as 4 times of it's compliment.

To Find :

We are asked to find the angle.

Let us take the angle as x

Now, the supplement of that angle would be 180 - x

And the complement of that angle would be 90 - x

According to the question,

The supplement is given as 4 times of it's complement.

Hence,

Supplement = 4 ( complement )

Writing this as an equation, we get,

___________________

The angle is 60.

The supplement of it is 180 - 60 = 120.

And the complement of that angle is 90 - 60 = 30