Question

Two opposite angles of the parallelogram are 3x – 5° and x + 45°. Find the angles of the parallelogram.

Answer 1

Given: Two opposite angles of the parallelogram are 3x – 5° and x + 45°.

Step-wise calculation:

1. Opposite angles in a parallelogram are equal and adjacent angles are supplementary.

2. Set the opposite angles equal:

3x – 5 = x + 45

3. Solve:

3x – x = 45 + 5

⇒ 2x = 50

⇒ x = 25

4. Evaluate the angles:

3x – 5 = 3(25) – 5

= 75 – 5

= 70° 

Also x + 45

= 25 + 45

= 70°

5. Adjacent angles

= 180° – 70°

= 110°

The angles of the parallelogram are 70°, 110°, 70°, 110°.