In a parallelogram, consecutive angles are supplementary and opposite angles are congruent. Using these properties, we can write a system of equations.

1.

2.

3.

Starting with equation 1.,

Substituting into equation 2.,

Using equation 3.,

In a parellelogram, consecutive angles are supplementary.

In a parallelogram, opposite angles are congruent.

In a parallelogram, consecutive angles are supplementary and opposite angles are congruent.

In a parallelogram, consecutive angles are supplementary and opposite angles are congruent.

In the above parallelogram, and are consecutive angles (i.e. next to each other). In a parallelogram, consecutive angles are supplementary, meaning they add to .

In a parallelogram, consecutive angles are supplementary. Thus,

In a parallelogram, consecutive angles are supplementary and opposite angles are congruent. Using these properties, we can write a system of equations. Because we have three variables, we will need three equations.

1.

2.

3.

Start with equation 1.

Now simplify equation 2.

Finally, simplify equation 3.

Note that we can plug this simplified equation 3 directly into the simplified equation 2 to solve for .

Now that we have , we can solve for using equation 1.

With , we can solve for using equation 3.

Now that we have and , we can solve for .

In parallelogram , and are opposite angles. In a parallelogram, opposite angles are congruent. This means these two angles are equal.

In a parallelogram, consecutive angles are supplementary. and are consecutive, so their sum is .