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Question

Prove that the bisectors of two adjacent supplementary angles include a right angle.

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Solution

Let AOB denote a straight line and let AOC and BOC be the supplementary angles.
Then, we have:
AOC=x° and BOC=180-x°
Let OE bisect AOC and OF bisect BOC.
Then, we have:
AOE=COE=12x° andBOF=FOC=12180-x°
Therefore,
COE+FOC=12x+12180°-x
=12x+180°-x=12180°=90°

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