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

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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.

The Angle Between The Bisectors Of Two Adjacent Supplementar...

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 adjacentsupplementary angles is

90^{\circ}

.

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