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Question
The bisectors of any two adjacent angles of a parallelogram intersect at
Options
30°
45°
60°
90°
Solution
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).
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