Question

The measure of two adjacent angles of a parallelogram are in the ratio 4:5 .Find the measure of each of the angles of the parallelogram.

Answer 1

Step-by-step explanation:

Given :-

The measure of two adjacent angles of a parallelogram are in the ratio 4:5 .

To find:-

Find the measure of each of the angles of the parallelogram?

Solution:-

Given that

The ratio of the measure of two adjacent angles of a parallelogram = 4:5

Let they be 4X° and 5X°

We know that

The sum of adjacent angles in a Parallelogram are supplementary.

=> 4X° + 5X° = 180°

=> 9X° = 180°

=> X° = 180°/9

=>X° = 20°

Now ,

4X° = 4(20°)=80°

5X°=5(20°)=100°

We know that

Opposite angles are equal in a Parallelogram

The opposite angle of 80° = 80°

The opposite angle of 100° = 100°

Answer:-

The all angles in the given Parallelogram are

80°,100° ,80° and 100°

Used formulae:-

In a Parallelogram,

• The sum of adjacent angles are supplementary.
• The opposite angles are equal.