Question

The greater of two supplementary angles exceeds the smaller by 18°. Find measures of these two angles.

Answer 1

Let the smaller angle be x

Greater angle = x + 18°

As the angles are supplementary,

So, Sum of angles = 180°

⇒ x + (x + 18°) = 180°

⇒ 2x + 18° = 180°

⇒ 2x = 180° − 18°

⇒ 2x = 162°

⇒ x = 81°

Greater angle = (x + 18°) = (81° + 18°) = 99° So, the measures of angles are 81° and 99°.