Question

Calculate all the angles of a parallelogram if one of its angles is twice its adjacent angle.​

Answer 1

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Given:-

• One angle of a parallelogram is twice of its adjacent angle.

We know that,

In a parallelogram, opposite angles are equal.

Let the angles are x° , 2x° , x° , 2x°

sum of the angles = 360°

x° + 2x° + x° + 2x° = 360°

6x° = 360°

x° = 60°

⟶ Therefore the angles are 60° , 120° , 60° , 120°.

Answer 2

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Let the two adjacent angles be x° and 2x° .

In a parallelogram, sum of the adjacent angles are 180°.

∴ x + 2x = 180°

⇒ 3x = 180°

⇒ x = 60°

Thus , the two adjacent angles are 120° and 60°. Hence, the angles of the parallelogram are 120°, 60°, 120° and 60°.