Question

In the adjacent parallelogram ABCD, AP ⊥ CD and AQ ⊥ BC. If x : y = 5 : 4, then find the angles of the parallelogram.

Answer 1

Given:

In parallelogram ABCD, adjacent angles are in the ratio x : y = 5 : 4 from the provided figure.

Adjacent interior angles of a parallelogram are supplementary and sum to 180°.

Step-wise calculation:

1. Let the two adjacent angles be 5k and 4k.

2. Because they are supplementary:

5k + 4k = 180°

3. So, 9k = 180°

⇒ k = 20°

4. Therefore, the two adjacent angles are

5k = 5 × 20°

= 100° 

And 4k = 4 × 20°

= 80°

5. In a parallelogram, the opposite angles are equal.

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

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