Question

the sum of the two opposite angles of a parallelogram is 120 degree find all the angles of the parallelogram.​

Answer 1

Answer:

The angles of the parallelogram are 60°, 60°, 120° and 120° respectively.

Step-by-step explanation:

Given:

• The sum of the two opposite angles of a parallelogram is 120°.

To find:

• All the angles of the parallelogram.

Solution:

Opposite angles of a parallelogram are equal.

Let the opposite angles be x°

We know that the sum of the two opposite angles of a parallelogram is 120°.

Then,

• x + x = 120°
• 2x = 120°
• x = 120/2
• x = 60°

Sum of all the angles of a parallelogram is equal to 360°.

Let the other two opposite angles of a parallelogram are a°.

• 120° + a° + a° = 360°
• 120° + 2a° = 360°
• 2a° = 360° - 120°
• 2a° = 240°
• a = 240/2
• a = 120°

Verification:

We know that the sum of all the angles of a parallelogram is equal to 360°, so

• = 60° + 60° + 120° + 120°
• = 120° + 240°
• = 360°

Hence verified!!

━━━━━━━━━━━━━━━━━━━━━

Answer 2

Step-by-step explanation:

given the ratio between the two adjacent angles of a parallelogram is 4 : 5

let the two adjacent angles of the paralelegram be 4x and 5x respectively.

we know that,

» sum of two adjacent angles in a parallelogram = 180°

➡ 4x + 5x = 180°

➡ 9x = 180°

➡ x = 180/9

➡ x = 20°

therefore the two adjacent angles are :-

4x = 4 × 20 = 80°

5x = 5 × 20 = 100°

now, also the opposite angles of a parallelogram is same. it's one of it's properties. opposite angles are same in a parallelogram.

hence, all the angles of the parallelogram are 80°, 100°, 80° and 100°