ACT Math : Plane Geometry

Study concepts, example questions & explanations for ACT Math

varsity tutors app store varsity tutors android store varsity tutors ibooks store

Example Questions

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

Parallelogram_4

In parallelogram  and . Find .

Possible Answers:

Correct answer:

Explanation:

In a parallelogram, consecutive angles are supplementary. Thus,

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

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 #3 : How To Find An Angle In A Parallelogram

Parallelogram_2

In parallelogram . What is ?

Possible Answers:

Correct answer:

Explanation:

In a parellelogram, consecutive angles are supplementary.

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

Parallelogram_2

In parallelogram . What is ?

Possible Answers:

Correct answer:

Explanation:

In a parallelogram, opposite angles are congruent.

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

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 #1 : How To Find An Angle In A Parallelogram

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 #1 : How To Find An Angle In A Parallelogram

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 #4 : How To Find An Angle In A Parallelogram

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 .

Example Question #11 : How To Find An Angle In A Parallelogram

Parallelogram_6

 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. 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 .

 

Learning Tools by Varsity Tutors