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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
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,
a+b=180o ....... (i)
After bisecting the angles with measures a and b we get the measures of that angles as a2 and b2 respectively.
From (i), we get
(a+b)/2=180o/2
a2+b2=90o
Now, the bisectors will form a triangle and sum of the angles of a triangles is 1800.
Measure of angle formed by bisectors =18090=90o.
Hence, option D is correct.

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