Question

The larger of two supplementary angles exceeds the smaller by 18 degrees. Choose the correct options.

• A. One of the angles is ${99}^{\circ }$
• B. One of the angles is ${85}^{\circ }$
• C. One of the angles is ${107}^{\circ }$
• D. One of the angles is ${81}^{\circ }$

Answer 1

Answer: (A), (D)

The correct options are
A

One of the angles is ${99}^{\circ }$

D

One of the angles is ${81}^{\circ }$

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 .... (ii)
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 ${81}^{\circ }$.