Question

the measures of two adjacent angle of a parallelogram are in the ratio 2:3 find the measure of each of the angle parallelogram​

Answer 1

Answer:

Given :-

Ratio of angles of parallelogram is 2 : 3.

To find :- All angles of parallelogram.

Solution :-

Let ABCD be a parallelogram.

Let angles of parallelogram be 'x'.

/_A = /_C = 2x°. .........(Opposite angles of parallelogram.)

/_B = /_D = 3x°.........(Opposite angles of parallelogram.)

/_A + /_B = 180° .......(Adjacent angles of parallelogram are supplementry)

2x° + 3x° = 180°

5x° = 180°

x = 36° ..........(1)

/_A = /_C = 72° ...........(From 1)

/_B = /_D = 108° ...........(From 1)

Answer :- Angles of parallelogram are 72° ; 108° ; 72° ; 108°.

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Answer 2

We know that ,

Opposite Sides of parallelogram are parallel...

So, the adjecent angle will be interior angles of the transversal....which has the sum 180°.

So, let 3x and 2x be the angles....

➜ 3x + 2x = 180°

➜ 5x = 180°

➜ x = 36°

So, the angles are ...

3x = 36 × 3 = 108°

2x = 2 × 36 = 72

Now ,

We know ,

opposite angles of parallelegram are equal...

So, the angles of parallelogram are 108°,72°,108°,72°.