The larger of two supplementary angles exceeds the smaller by 18 degre

1.	The larger of two supplementary angles exceeds the smaller by 18 degrees. Find them.
Answer» 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°.

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

Answer»

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°.