Question:
In a parallelogram ABCD, ∠D = 135°, determine the measure of ∠A and ∠B.
Solution:
In $a$ parallelogram, opposite angles have the same value.
$\therefore \angle \mathrm{D}=\angle \mathrm{B}$
$=135^{\circ}$
Also, $\angle \mathrm{A}+\angle \mathrm{B}+\angle \mathrm{C}+\angle \mathrm{D}=360^{\circ}$
$\angle \mathrm{A}+\angle \mathrm{D}=180^{\circ}$ (opposite angles have the same value)
$\angle \mathrm{A}=180^{\circ}-135^{\circ}=45^{\circ}$
$\angle \mathrm{A}=45^{\circ}$