In a parallelogram ABCD, ∠D = 135°,


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


In $a$ parallelogram, opposite angles have the same value.

$\therefore \angle \mathrm{D}=\angle \mathrm{B}$


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)

$\angle \mathrm{A}=180^{\circ}-135^{\circ}=45^{\circ}$

$\angle \mathrm{A}=45^{\circ}$

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