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°.
