In a parallelogram ABCD, ∠D= 135°, determine the measure of ∠A

1.	In a parallelogram ABCD, ∠D= 135°, determine the measure of ∠A and ∠B.
Answer» Given, one of the adjacent angle ∠D = 135° Let other adjacent angle ∠A be = x° We know that sum of adjacent angles = 180° x° + 135° = 180° x° = 180° – 135° = 45° ∠A = x° = 45° We know that measure of opposite angles are equal in a parallelogram. So, ∠A = ∠C = 45° And ∠D = ∠B = 135°

In a parallelogram ABCD, ∠D= 135°, determine the measure of ∠A and ∠B.

Answer»

Given, one of the adjacent angle ∠D = 135°

Let other adjacent angle ∠A be = x°

We know that sum of adjacent angles = 180°

x° + 135° = 180°

x° = 180° – 135°

= 45°

∠A = x° = 45°

We know that measure of opposite angles are equal in a parallelogram.

So, ∠A = ∠C = 45°

And ∠D = ∠B = 135°