Question

The bisectors of any two adjacent  angles of a parallelogram intersect at

Options

• 30°

• 45°

• 60°

• 90°

Answer 1

Let the figure be as follows:

ABCD is a parallelogram.

We have to find ∠DNA

AN and AD is the bisectors of ∠A and ∠D.

Therefore,

`∠DAN = 1/2 ∠A` …… (i)

And

 `∠ADN = 1/2 ∠D` …… (ii)

We know that AB || DC.

Therefore, the sum of consecutive interior angles must be supplementary.

`∠A + ∠D = 180°`

`1/2∠A + 1/2∠D = 180°/2` 

From (i) and (ii), we get

∠DAN + ∠ADN = 90°…… (iii)

By angle sum property of a triangle:

∠DAN + ∠DAN + ∠ADN = 180°

                   ∠DNA + 90° = 180°

                             ∠DNA = 180° - 90°

                             ∠DNA = 90°

Hence the correct choice is (d).