Question

The larger of the two supplementary angles exceeds the smaller by ${18}^{\circ }$. Find them.

Answer 1

Let $x$ & $y$ be the angles. [$x>y$]

Since the angles are supplementary, we have

$x+y=180$

$x=180-y\dots \dots \left(i\right)$

According to given condition, we have

$x-y=18\dots \dots \left(ii\right)$ [$\because$ Difference between the two angle is ${18}^{\circ }$ ]

Substituting value of ${}^{\prime }{x}^{\prime }$ in $\left(ii\right),$ we get
$\Rightarrow 180-y-y=18$

$\Rightarrow -2y=-162$

$\Rightarrow y=81$

Now, $x=180-y$

$\Rightarrow x=180-81$

$\Rightarrow x=99$

$\therefore x=99,y=81$