How to find the value of x in a parallelogram

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Correct answer:

Explanation:

We can start this problem by drawing the height and labeling the lengths with the given values.

When we do this, we can see that we have drawn a triangle inside the paralellogram including . Because we know the lengths of two sides of this triangle, we can use trigonometry to find .

With respect to 

Correct answer:

Explanation:

In a parallelogram, consecutive angles are supplementary. Thus,

 is a parallelogram. Find .

Correct answer:

Explanation:

In a parallelogram, consecutive angles are supplementary (i.e. add to ) and opposite angles are congruent (i.e. equal). Using these properties, we can write a system of equations.

1. 

2. 

Starting with equation 1.,

Now substituting into equation 2.,

Finally, because opposite angles are congruent, we know that .

 is a parallelogram. Find .

Correct answer:

Explanation:

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 parallelogram , . What is ?

Correct answer:

Explanation:

In a parellelogram, consecutive angles are supplementary.

In parallelogram , . What is ?

Correct answer:

Explanation:

In a parallelogram, opposite angles are congruent.

 is a parallelogram. Find .

Correct answer:

Explanation:

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

In parallelogram ,  . What is 

Correct answer:

Explanation:

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 parallelogram , . What is ?

Correct answer:

Explanation:

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

In parallelogram , what is the sum of  and ?

Correct answer:

Explanation:

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

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What is the formula for parallelograms?

How do you find the value of x?