Question

The larger of two supplementary angles exceeds the smaller by 18 degrees. Find the angles. [3 MARKS]

Answer 1

Concept : 1 Mark
Application : 1 Mark
Calculation : 1 Mark

Let $x$ & $y$ be the angles.

Since the angles are supplementary,

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

According to given condition,

$x-y=18\dots \dots \left(ii\right)$

Solving (i) and (ii) we get,

$x=180-y$ [From (i)]

Substituting value of $x$ in (ii)

$x-y=18$

$180-y-y=18$

$-2y=-162\Rightarrow y=81$

Now, $x=180-y$

$\Rightarrow x=180-81$

$\Rightarrow x=99$

$\therefore x=99,y=81$