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Question

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


A
30
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B
45
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C
60
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D
90
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Solution

The correct option is D $$90^{\circ}$$
In a parallelogram, opposite angles are congruent(i.e. are of equal length).
Also, the opposite angles are of same measure.
Whereas the adjacent angles are supplementary(add up to 180 degrees). 
Let $$a$$ and $$b$$ be measures of any two adjacent angles of a parallelogram,
$$\implies a+b=180^{o}$$ ....... (i)
After bisecting the angles with measures $$a$$ and $$b$$ we get the measures of that angles as $$\dfrac{a}{2}$$ and $$\dfrac{b}{2}$$ respectively.
From (i), we get
$$(a+b)/2=180^{o}/2$$
$$\implies \dfrac{a}{2}+\dfrac{b}{2}=90^{o}$$
Now, the bisectors will form a triangle and sum of the angles of a triangles is $$180^{0}$$.
$$\therefore$$ Measure of angle formed by bisectors $$=180-90=90^{o}$$.
Hence, option D is correct.

Maths

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