91Ó°ÊÓ

We are given two supplementary angles and larger angle is $18$less than twice the measure of the smaller angle.

Let the smaller angle be $x$and larger angle be$y$

We know that the sum of supplementary angles is equal to ${180}^{∘}$. so

$x+y={180}^{∘}$

Also, the other equation will be $y=2x-18$.

Putting the value of $y$in first equation, we get

localid="1644389081295" $$\begin{gathered} x+2x-18={180}^{∘} \\ 3x-18={180}^{∘} \end{gathered}$$

Adding $18$both sides, we get

localid="1644389531085" $3x={198}^{∘}$

Dividing by $3$,

$x={66}^{∘}$

Putting the value of $x$in second equation, we get

$$\begin{gathered} y=2×66-18 \\ ={114}^{∘} \end{gathered}$$

Checking the solution by putting the value of $x,y$in the equations, we get

$$\begin{gathered} x+y={180}^{∘} \\ {66}^{∘}+{114}^{∘}={180}^{∘} \\ {180}^{∘}={180}^{∘} \\ y=2x-14 \\ {114}^{∘}=2\left({66}^{∘}\right)-18 \\ {114}^{∘}={132}^{∘}-18 \\ {114}^{∘}={114}^{∘} \end{gathered}$$

This is true, hence the solution is correct.