Question

find the measure formed by the bisectors of two adjacent angles of a parallelogram
​

Answer 1

Step-by-step explanation:

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=180

o

....... (i)

After bisecting the angles with measures a and b we get the measures of that angles as

2

a

and

2

b

respectively.

From (i), we get

(a+b)/2=180

o

/2

⟹

2

a

+

2

b

=90

o

Now, the bisectors will form a triangle and sum of the angles of a triangles is 180

0

.

∴ Measure of angle formed by bisectors =180−90=90

o

.

Hence, option D is correct.