Question

One of the exterior and interior angles of a parallelogram are in ratio 2:3 . Find all angles of the parallelogram

Answer 1

Answer:

Let the //gm be ABCD.

Extend a line E from D.

Now,

angle BDC + angle BDE= 180 (linear pair)

given,

ratio= 2:3

therefore,

2x+3x=180

5x=180

x=36

Now,

angle BDC = 2x=2×36= 72

We know that,

Opposite angles of a //gm are equal.

So, angle D=angle A and angle C = angle B

since we have found angle D, angle A also equals 72.

Let angle B and angle C be x

x+x+72+72=360 ( property of //gm)

2x+144=360

2x=360-144

2x=216

x=216÷2

x=108

angle A= 72

angle B=108

angle C=72

angle D=108

*this can also be solved through interior alternate angles property*

Answer 2

Answer:

A. T. Q

2x+3x=180

5x=180

=36

2*36=72

angle 1 =angle 3=72°

<1+<2=180°

<2=180-72

<2 = 108°

<2 =<4=108°

hence done

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