The angle between the bisectors of two adjacent supplementary angles is a right angle. Options: A . &nbsp True B . &nbsp False C . &nbsp Right angled triangle D . &nbsp Equilateral triangle

The angle between the bisectors of two adjacent supplementary angles is a right

Question

The angle between the bisectors of two adjacent supplementary angles is a right angle.

Options:

A . True

B . False

C . Right angled triangle

D . Equilateral triangle

Answer: Option A
:
A

Let $∠ A$ and $∠ B$ be adjacent supplementary angles as shown in the figure.

Then, $∠ A + ∠ B = 180^{\circ}$
The bisectors of the angles are drawn. We have to find $∠ 1 + ∠ 2$ .
$∠ 1 + ∠ 2 = (\frac{∠ A}{2} + \frac{∠ B}{2})$
$= \frac{180}{2} = 90^{\circ}$
Hence, the angle between the bisectors of adjacent supplementary angles is $90^{\circ}$ .

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