Question

two adjacent angle of a paralleogram are in the ratio 4:5. find the measure of each of it's angles hint adjacent angle of a paralleogram are supplementary​

Answer 1

Answer:

The angles are 80° and 100°

Step-by-step explanation:

Given :-

Two adjacent angles of a parallelogram are in ratio 4:5

To Find :-

Measure of each angle.

Hint :-

Adjacent angles of a parallelogram are supplementary.

Solution :-

Using the Hint, we can say that the adjacent sides ∠A and ∠D = 180.

It is also given that the adjacent sides are in ratio 4 : 5,

So,

5x + 4x = 180

9x = 180

x = 180 / 9

x = 20

Therefore,

∠A = 4x = 4 ( 20 ) = 80°

∠D = 5x = 5 ( 20 ) = 100°

We know that, opposite angle of parallelogram are equal so,

The opposite angle of ∠A is ∠C so ∠C = 80°

similarly, opposite angle of ∠D is ∠B = 100°

Answer 2

Answer :- Adjacent angle of parallelogram are 80° and 100°.

Given :- Adjacent angle of parallelogram is in 4:5

To Find :- Adjacent angle of parallelogram

Solution :-

Let us considered Angle A and Angle B are adjacent angle.

We known adjacent angle are supplementary = 180°

4x + 5x = 180°

9x = 180°

x = 180/9

x = 20

Substituting x = 20

Angle A = 4x = 4(20) = 80°

Angle B = 5x = 5(20) = 100°

Therefore, the adjacent angle of parallelogram is 80° and 100° respectively.