The larger of two supplementary angles exceeds the smaller by 18 degrees. Find them.

Given: The larger of two supplementary angles exceeds the smaller by 18 degrees.

To find: The measure of both angles.

solution: 

Let the larger angle be ‘a’ and the smaller angle be ‘b’.

Given, larger of two supplementary angles exceeds the smaller by 18 degrees.

⇒ a = b + 18

⇒ a - b = 18 ...... (1)


The sum of supplementary angles is 180°.


⇒a + b = 180.....(2)

Adding the equations 1 and 2 we get,

a-b+a+b=18+180

⇒ 2a = 198

⇒ a = 99°

Put the value of b in eq. 1 to get,

99-b=18

⇒ -b=18-99

⇒ -b=-81

⇒ b=81

Thus, b = 81°

Hence the measure of smaller angle is 81° and larger angle is 99°.