Question

The measures of two adjacent angles of a parallelogram are in the ratio 2:3 . Find the measure of each of the angles of the parallelogram.​

Answer 1

Question:-

The measures of two adjacent angles of a parallelogram are in the ratio 2:3 . Find the measure of each of the angles of the parallelogram .

Required Answer:-

Given:-

• The ratio two adjacent angles of the parallelogram is 2:3

To Find:-

• Each angles of the parallelogram.

Solution:-

Parallelogram:- A parallelogram is a two-dimensional geometrical shape, whose sides are parallel to each other. It is a type of polygon having four sides (also called quadrilateral), where the pair of parallel sides are equal in length.

Let,

• Common factor of the ration be x

Therefore,

• → 1st angle = 2x
• → 2nd angle = 3x

We know that:-

• The opposite angles of the parallelogram are equal.

Therefore,

• → 3rd angle = 2x
• → 4rth angle = 3x

• Hence, the angles of the parallelogram are 2x,3x,2x and 3x

Remember that:-

• Total sum of the interior angles of any polygon with four sides is 360°

According to this, we can write:-

2x + 3x + 2x + 3x = 360

=> 10x = 360

=> x = 360/10

=> x = 36

• Hence, x = 36

Finding the angles:-

~~~1st angle and 3rd angle = 2x = 2*36 = 72°

~~~2nd angle and 4th angel = 3x = 3*36 = 108°

★ Hence, the angles are 72° , 108°, 72°, 108°