Question

Form the pair of linear equations for the following problems and find their solution by substitution method:
The larger of two supplementary angles exceeds the smaller by 18 degrees. Find them.

Answer 1

Let the larger angle = x
Smaller angle = y
As both angles are supplementary,
x + y = 180
$\Rightarrow$ x = 180 - y .... (i)
Difference is 18 degrees.
So, x - y = 18
$\Rightarrow$ x = 18 + y .... (i)
Substituting the value of x in equation (i) we get,
$\Rightarrow$ 18 + y = 180 - y
$\Rightarrow$ - y - y = 18 - 180
$\Rightarrow$ - 2y = -162
$\Rightarrow$ $y=\frac{-162}{-2}$
$\Rightarrow$ y = 81
Substituting the value of y in equation (i), we get,
$\Rightarrow$ x = 180 - 81 = 99
Hence, the angles are ${99}^{\circ }$ and ${81}^{\circ }$.