Question

Measures (in degrees) of two supplementary angles are consecutive odd integers. Find the angles.

Answer 1

Let one angle be 2x + 1, then the other angle is 2x + 3.

We know that the sum of the measures of the supplementary angles is 180°.

According to the question,

2x + 1 + 2x + 3 = 180°

⇒ 4x + 4 = 180°

⇒ 4x = 180° – 4 = 176°

⇒ x = `176^circ/4` = 44°

∴ 2x + 1 = 2 × 44° + 1 = 88° + 1 = 89°

And 2x + 3 = 2 × 44° + 3 = 88° + 3 = 91°

Thus, one angle is 89° and the other is 91°.