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Question
Measures (in degrees) of two supplementary angles are consecutive odd integers. Find the angles.
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Solution
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 other is 91°.
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