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

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

Let other adjacent angle ∠A be = x°

We know that sum of adjacent angles = 180°

x^o + 135^o = 180^o

x^o = 180^o – 135^o

     = 45^o

∠A = x^o = 45^o

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

So, ∠A = ∠C = 45^o

And ∠D = ∠B = 135^o

So , ∠A + ∠B = 45^o + 135^o = 180^o