Question

3. If one angle of a parallelogram is 36 less than twice its adjacent angle, then
find the angles of parallelogram,​

Answer 1

The four angles of parallelogram is 72°, 72° & 108°, 108°

Step-by-step explanation:

We know,

The sum of adjacent sides of parallelogram is 180°

So ,

Let the adjacent angle be X .

x + (2x - 36) = 180°

3x = 180°+36°

3x = 216°

x = 216/3

x = 72°

If one angle is of 72° then the another angle is (180 - 72) = 108°

So, The four angles of parallelogram is 72°, 72° & 108°, 108°

Answer 2

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GiveN:

• If one angle of a parallelogram is 36 less than twice its adjacent angle.

To FinD:

• All the angles of parallelogram?

Step-by-Step Explanation:

We know that,

The adjacent angles of a parallelogram add upto 180°. That means they are supplementary.

Let one of the angle be x, then the other angle will be 2x - 36. Their sum will be 180°.

⇒ x + 2x - 36 = 180°

⇒ 3x - 36° = 180°

⇒ 3x = 216°

⇒ x = 216° / 3

⇒ x = 72°

Then, adjacent angle will be

= 2(72°) - 36°

= 144° - 36°

= 108°

Hence,

• The angles of the parallelogram are 108°, 72°, 108° and 72° because the opposite angles are equal and the adjacent angles are supplementary.