Question

Find the measure of all the angles of a parallelogram if one angle is 24 degree less than twice the smallest angle

Answer 1

Hi,

We know that ,

In a parallelogram sum adjacent

angles are supplementary and

Opposite angles are equal.

Let ABCD is a parallelogram ,

Let smallest angle < A = x°

x + 2x - 24 = 180°

3x = 180 +24

3x = 204

x = 204/3

x = 68°

Therefore ,

<A = <C = x = 68°

<B = <D = 2x - 24

= 2 × 68 - 24

= 136 - 24

= 112°

I hope this helps you.

:)

Answer 2

Let the Parallelogram be ABCD
angle A+angle B + angle C+angle D=360

angle A+angle B+ angle A+angle B=360
(opposite angles of paralellogram are equal)

2(angleA+angle B) =360
angle A+angle B=180................. (1)
Now,
According to question
2(angle B) = angleA +24
2angleB-angleA=24....................(2)

Adding equation 1 and 2, we get
3 angle B =204
angle B = 68
angle A = 112
angle C = 112
angle D = 68