Question

The measure of two adjacent angle of parallelogram are in the ratio 3:2 . find the measure of each of the angle of parallelogram.


please give full solutions..​

Answer 1

Given:

The measure of two adjacent angles of a parallelogram is in ratio 3:2

To be found:

The measure of all angles of the parallelogram.

$\star$ Here are some properties of a parallelogram-

• The sum of two adjacent angles of a parallelogram is 180°.
• The opposite sides of the parallelogram are equal and parallel.
• The opposite angles of the parallelogram are equal.

So,

Let one angle be 3x and other 2x

As

• The opposite angles of the parallelogram are equal

Then we have 2 angles as '3x' degree and 2 angles as '2x' degree. [There are four interior angles in a parallelogram]

Now,

As they are adjacent so,

⇒ 3x +  2x = 180

⇒ 5x = 180

⇒ x = 180 ÷ 5

⇒ x = 36

So,

The angles are

3x = 3 × 36 = 108°

And

2x = 2 × 36 =  72°

Now,

We have two same angles as 108° and two same angles as 72°

Hence

The angles of the parallelogram are 108°, 108°, 72°, and 72°

Answer 2

SOLUTION:-

Given

• Two adjacent angle of llgm are in ⠀⠀ratio 3:2

To find

• All angles of llgm

Explanation

Let Two adjacent angles A or B of llgm ABCD be 3x and 2x respectively.

Since

The adjacent angles of a llgm are Supplementary.

∠A+∠B= 180°

➡️ 3x+2x =180°

➡️ 5x=180°

➡️ x=180°/5

➡️ x= 36°

Angles are ⤵️

3x = 3×36° = 108°

2x = 2×36° = 72°

Since

Opposite Angles are equal in llgm

Therefore

∠C= ∠A= 108°

And

∠D= ∠B= 72°

Hence,

•∠A=108°

•∠B=72°

•∠C= 108°

•∠D= 72°

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