The bisectors of two adjacent supplementary angles are always at

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Solution

Let two adjacent supplementary angles are $∠ P O Q$ and $∠ R O Q$ such that $O A$ and $O B$ are the angle bisectors

$∴ ∠ 1 + ∠ 2 = \frac{1}{2} ∠ P O R + \frac{1}{2} ∠ Q O R$

$= \frac{1}{2} (∠ P O R + ∠ Q O R)$

$= \frac{1}{2} (180^{\circ})$

$= 90^{\circ}$

Hence, the bisectors of two adjacent supplementary angles are always at right angle.

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The bisectors of two adjacent supplementary angles are always at

Let two adjacent supplementary angles are ∠POQ and ∠ROQ such that OA and OB are the angle bisectors ∴∠1+∠2=12∠POR+12∠QOR =12(∠POR+∠QOR) =12(180∘) =90∘ Hence, the bisectors of two adjacent supplementary angles are always at right angle.