# ACT Math : Parallelograms

## Example Questions

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### Example Question #1 : How To Find An Angle In A Parallelogram

In parallelogram  and the height is .  What is ?

Possible Answers:

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 , we know the values of the opposite and hypotenuse sides of the triangle. Thus, we can use the sine function to solve for .

### Example Question #2 : How To Find An Angle In A Parallelogram

In parallelogram  and . Find .

Possible Answers:

Correct answer:

Explanation:

In a parallelogram, consecutive angles are supplementary. Thus,

### Example Question #3 : How To Find An Angle In A Parallelogram

is a parallelogram. Find .

Possible Answers:

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 .

### Example Question #4 : How To Find An Angle In A Parallelogram

is a parallelogram. Find .

Possible Answers:

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.,

### Example Question #5 : How To Find An Angle In A Parallelogram

In parallelogram . What is ?

Possible Answers:

Correct answer:

Explanation:

In a parellelogram, consecutive angles are supplementary.

### Example Question #6 : How To Find An Angle In A Parallelogram

In parallelogram . What is ?

Possible Answers:

Correct answer:

Explanation:

In a parallelogram, opposite angles are congruent.

### Example Question #7 : How To Find An Angle In A Parallelogram

is a parallelogram. Find .

Possible Answers:

Correct answer:

Explanation:

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

### Example Question #8 : How To Find An Angle In A Parallelogram

In parallelogram . What is

Possible Answers:

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 .

### Example Question #9 : How To Find An Angle In A Parallelogram

In parallelogram . What is ?

Possible Answers:

Correct answer:

Explanation:

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

### Example Question #10 : How To Find An Angle In A Parallelogram

In parallelogram , what is the sum of  and ?

Possible Answers:

Correct answer:

Explanation:

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

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