Question

Two adjacent angles of a parallelogram are 2x + 10° and 4x – 40°. Find the angles of the parallelogram.

Answer 1

Given: Two adjacent angles are 2x + 10° and 4x – 40°.

Step-wise calculation:

1. Adjacent angles in a parallelogram sum to 180°:

(2x + 10) + (4x – 40) = 180°

2. Combine like terms:

6x – 30 = 180°

3. Solve for x:

6x = 210 

⇒ x = 35

4. Find each angle:

First angle

= 2x + 10 

= 2(35) + 10

= 80°

Second angle

= 4x – 40

= 4(35) – 40

= 100°

5. Opposite angles are equal.

So, the four angles are 80°, 100°, 80°, 100°.

The angles of the parallelogram are 80°, 100°, 80° and 100°.