Question

The sum of two opposite angles of a parallelogram is 120°. Find the measure of each of its angles.​

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:

The 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°

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

Let the other two opposite angles of a parallelogram be 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!!

━━━━━━━━━━━━━━━━━━━━━