ACT Math : Parallelograms

Study concepts, example questions & explanations for ACT Math

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Example Questions

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Example Question #1 : Parallelograms

Parallelogram_2

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.

Parallelogram_3

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 : Parallelograms

Parallelogram_4

In parallelogram  and . Find .

Possible Answers:

Correct answer:

Explanation:

In a parallelogram, consecutive angles are supplementary. Thus,

Example Question #3 : Parallelograms

Parallelogram_5

 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 : Parallelograms

Parallelogram_7

 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 : Parallelograms

Parallelogram_2

In parallelogram . What is ?

Possible Answers:

Correct answer:

Explanation:

In a parellelogram, consecutive angles are supplementary.

Example Question #6 : Parallelograms

Parallelogram_2

In parallelogram . What is ?

Possible Answers:

Correct answer:

Explanation:

In a parallelogram, opposite angles are congruent.

Example Question #7 : Parallelograms

Parallelogram_8

 is a parallelogram. Find .

Possible Answers:

Correct answer:

Explanation:

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

 

Example Question #8 : Parallelograms

Parallelogram_2

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 : Parallelograms

Parallelogram_2

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 : Parallelograms

Parallelogram_2

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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