Question

Find the measures of supplementary angles such that the larger angle is
four times the smaller angle
pls help just the equation

Answer 1

Answer :

36° and 144°

_______________________

As per the provided information in the given question, we have :

• The measures of supplementary angles such that the larger angle is four times the smaller angle.

We are asked to calculate the measures of the supplementary angles.

Let us assume the smaller angle as x°.

$\longmapsto \rm { Smaller \; angle = x^\circ}$

According to the question,

• The larger angle is four times the smaller angle.

$\longmapsto \rm { Larger \; angle = 4x^\circ}$

We know that, supplementary angles are those angles whose sum is 180°. So,

$\longmapsto \rm { x^\circ + 4x^\circ = 180^\circ}$

Performing addition of the like terms in L.H.S.

$\longmapsto \rm { 5x^\circ = 180^\circ}$

Transposing 5 from L.H.S to R.H.S. Its arithmetic operator will get changed after transposition.

$\longmapsto \rm { x^\circ = \cancel{\dfrac{180^\circ}{5}} }$

Performing division.

$\longmapsto \rm { x^\circ = 36^\circ}$

Therefore,

$\longmapsto \rm { Smaller \; angle = x^\circ}$

$\longmapsto \bf \underline { Smaller \; angle = 36^\circ}$

And,

$\longmapsto \rm { Larger \; angle = 4x^\circ}$

Substituting the value of x.

$\longmapsto \rm { Larger \; angle = 4(36)^\circ}$

$\longmapsto \bf \underline { Larger \; angle = 144^\circ}$

∴ The measures of supplementary angles are 36° and 144°.