Question

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

A
30
B
45
C
60
D
90

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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