Call Now to Set Up Tutoring:

(888) 888-0446

ACT Math : Quadrilaterals

Study concepts, example questions & explanations for ACT Math

Create An Account

All ACT Math Resources

14 Diagnostic Tests 767 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #302 : Act Math

Given the height of a trapezoid is and a base length is , what is the length of the other base if the area of the trapezoid is ?

Possible Answers:

Correct answer:

Explanation:

Write the formula used to find the area of a trapezoid.

$A=\frac{1}{2}h(b1+b2)$

Substitute the given information to the formula and solve for the unknown base.

$10=\frac{1}{2}(1)(1+b2)$

20=1+b2

b2=19

Report an Error

Example Question #1 : How To Find The Length Of The Side Of A Trapezoid

ABCD is an isosceles trapezoid that is bisected by $\overline{EF}$ .

$\overline{AB} \left | \right | \overline{EF} \left | \right | \overline{DC}$ . If $\overline{AE} = 4$ , $\overline{ED} = 6$ , and $\overline{DC} = 18$ , then what is the length of $\overline{EF}$ ?

Possible Answers:

Correct answer:

Explanation:

We know that all three horizontal lines are parallel to one another. By definition, we can set up a ratio between the lengths of the sides provided to us in the question and the lengths of the two parallel lines:

$\frac{AE}{ED} = \frac{EF}{DC}$

Once we substitute the given information, we get

$\frac{4}{6}=\frac{EF}{18}$

We cross multiply to solve for EF

$EF = \frac{(4)(18)}{6}$

Report an Error

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

Parallelogram_2

In parallelogram ABCD , $\overline{AB} = 15$ and the height is . What is $\measuredangle A$ ?

Possible Answers:

$51.3^{\circ}$

$38.7^{\circ}$

$36.9^{\circ}$

$90.0^{\circ}$

$53.1^{\circ}$

Correct answer:

$53.1^{\circ}$

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 $\measuredangle A$ . Because we know the lengths of two sides of this triangle, we can use trigonometry to find $\measuredangle A$ .

With respect to $\measuredangle A$ , we know the values of the opposite and hypotenuse sides of the triangle. Thus, we can use the sine function to solve for $\measuredangle A$ .

$\sin \left (\measuredangle A\right ) = \frac{\textup{opposite}}{\textup{hypotenuse}}$

$\sin \left (\measuredangle A\right ) = \frac{12}{15}= 0.8$

$\measuredangle A = \arcsin\left ( 0.8\right ) = 53.1^{\circ}$

Report an Error

Example Question #1 : Parallelograms

Parallelogram_4

In parallelogram ABCD , $\measuredangle B = \left (2x + 15 \right )^{\circ}$ and $\measuredangle C = x^{\circ}$ . Find .

Possible Answers:

115

Correct answer:

Explanation:

In a parallelogram, consecutive angles are supplementary. Thus,

$\measuredangle B + \measuredangle C = 180^{\circ}$

$\left ( 2x + 15\right ) + x = 180$

3x + 15 = 180

3x = 165

x = 55

Report an Error

Example Question #1 : Parallelograms

Parallelogram_5

ABCD is a parallelogram. Find .

Possible Answers:

119

Correct answer:

Explanation:

In a parallelogram, consecutive angles are supplementary (i.e. add to $180^{\circ}$ ) and opposite angles are congruent (i.e. equal). Using these properties, we can write a system of equations.

1. $\measuredangle B = \measuredangle D$

2. $\measuredangle C + \measuredangle D = 180^{\circ}$

Starting with equation 1.,

2x + 3 = y + x

x + 3 = y

x = y - 3

Now substituting into equation 2.,

$y + \left ( y + x\right ) = 180$

2y + x = 2y + (y - 3) = 180

3y - 3 = 180

3y = 183

y = 61

Finally, because opposite angles are congruent, we know that $\measuredangle A = \measuredangle C$ .

z = y

z = 61

Report an Error

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

Parallelogram_7

ABCD 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. $\measuredangle B =\measuredangle D$

2. $\measuredangle B + \measuredangle C = 180^{\circ}$

3. $\measuredangle A = \measuredangle C$

Starting with equation 1.,

x = 4y - x

2x = 4y

x = 2y

Substituting into equation 2.,

x + y = 180

2y + y = 180

3y = 180

y = 60

Using equation 3.,

z = y

z = 60

Report an Error

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

Parallelogram_2

In parallelogram ABCD , $\measuredangle C = 75^{\circ}$ . What is $\measuredangle D$ ?

Possible Answers:

$90^{\circ}$

$115^{\circ}$

$125^{\circ}$

$75^{\circ}$

$105^{\circ}$

Correct answer:

$105^{\circ}$

Explanation:

In a parellelogram, consecutive angles are supplementary.

$\measuredangle C + \measuredangle D = 180^{\circ}$

$75^{\circ} + \measuredangle D = 180^{\circ}$

$\measuredangle D = 105^{\circ}$

Report an Error

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

Parallelogram_2

In parallelogram ABCD , $\measuredangle D = 125^{\circ}$ . What is $\measuredangle B$ ?

Possible Answers:

$120^{\circ}$

$90^{\circ}$

$125^{\circ}$

$180^{\circ}$

$115^{\circ}$

Correct answer:

$125^{\circ}$

Explanation:

In a parallelogram, opposite angles are congruent.

$\measuredangle B = \measuredangle D$

$\measuredangle B = 125^{\circ}$

Report an Error

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

Parallelogram_8

ABCD is a parallelogram. Find .

Possible Answers:

85.5

Correct answer:

Explanation:

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

$\measuredangle A + \measuredangle D = 180^{\circ}$

$z + \left ( 2z + 9\right ) = 180$

3z + 9 = 180

3z = 171

z = 57

$\measuredangle A = \measuredangle C$

z = y

57 = y

Report an Error

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

Parallelogram_2

In parallelogram ABCD , $\measuredangle A = 45^{\circ}$ . What is $\measuredangle B?$

Possible Answers:

$180^{\circ}$

$90^{\circ}$

$120^{\circ}$

$135^{\circ}$

$45^{\circ}$

Correct answer:

$135^{\circ}$

Explanation:

In the above parallelogram, $\measuredangle A$ and $\measuredangle B$ are consecutive angles (i.e. next to each other). In a parallelogram, consecutive angles are supplementary, meaning they add to $180^{\circ}$ .

$\measuredangle A + \measuredangle B = 180^{\circ}$

$45^{\circ} + \measuredangle B = 180^{\circ}$

$\measuredangle B = 135^{\circ}$

Report an Error

View ACT Math Tutors

Robert
Certified Tutor

Rensselaer Polytechnic Institute, Bachelors, Electrical Engineering. Brooklyn Polytechnic, Masters, Computer Science.

View ACT Math Tutors

Mohammad
Certified Tutor

Rutgers University-New Brunswick, Bachelor of Science, Mathematics. Rutgers University-New Brunswick, Master of Science, Stat...

View ACT Math Tutors

Joy
Certified Tutor

Boston University, Bachelor in Arts, Conservation Biology.

All ACT Math Resources

14 Diagnostic Tests 767 Practice Tests Question of the Day Flashcards Learn by Concept

ACT Math Tutors in Top Cities:

Atlanta ACT Math Tutors, Austin ACT Math Tutors, Boston ACT Math Tutors, Chicago ACT Math Tutors, Dallas Fort Worth ACT Math Tutors, Denver ACT Math Tutors, Houston ACT Math Tutors, Kansas City ACT Math Tutors, Los Angeles ACT Math Tutors, Miami ACT Math Tutors, New York City ACT Math Tutors, Philadelphia ACT Math Tutors, Phoenix ACT Math Tutors, San Diego ACT Math Tutors, San Francisco-Bay Area ACT Math Tutors, Seattle ACT Math Tutors, St. Louis ACT Math Tutors, Tucson ACT Math Tutors, Washington DC ACT Math Tutors

Popular Courses & Classes

SSAT Courses & Classes in Seattle, ACT Courses & Classes in Los Angeles, GRE Courses & Classes in Washington DC, GMAT Courses & Classes in San Diego, ACT Courses & Classes in Washington DC, ACT Courses & Classes in Denver, Spanish Courses & Classes in Philadelphia, SSAT Courses & Classes in Denver, MCAT Courses & Classes in Miami, LSAT Courses & Classes in Denver

Popular Test Prep

ACT Test Prep in San Francisco-Bay Area, ACT Test Prep in Denver, SSAT Test Prep in Dallas Fort Worth, SAT Test Prep in Denver, ISEE Test Prep in Denver, ACT Test Prep in Los Angeles, SSAT Test Prep in San Francisco-Bay Area, MCAT Test Prep in Philadelphia, ACT Test Prep in Dallas Fort Worth, GRE Test Prep in Seattle

DMCA Complaint

If you believe that content available by means of the Website (as defined in our Terms of Service) infringes one or more of your copyrights, please notify us by providing a written notice (“Infringement Notice”) containing the information described below to the designated agent listed below. If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available by means of the most recent email address, if any, provided by such party to Varsity Tutors.

Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects.org.

Please be advised that you will be liable for damages (including costs and attorneys’ fees) if you materially misrepresent that a product or activity is infringing your copyrights. Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney.

Please follow these steps to file a notice:

You must include the following:

A physical or electronic signature of the copyright owner or a person authorized to act on their behalf; An identification of the copyright claimed to have been infringed; A description of the nature and exact location of the content that you claim to infringe your copyright, in \ sufficient detail to permit Varsity Tutors to find and positively identify that content; for example we require a link to the specific question (not just the name of the question) that contains the content and a description of which specific portion of the question – an image, a link, the text, etc – your complaint refers to; Your name, address, telephone number and email address; and A statement by you: (a) that you believe in good faith that the use of the content that you claim to infringe your copyright is not authorized by law, or by the copyright owner or such owner’s agent; (b) that all of the information contained in your Infringement Notice is accurate, and (c) under penalty of perjury, that you are either the copyright owner or a person authorized to act on their behalf.

Send your complaint to our designated agent at:

Charles Cohn Varsity Tutors LLC
101 S. Hanley Rd, Suite 300
St. Louis, MO 63105

Or fill out the form below:

Do not fill in this field

Contact Information

* Full legal name

Company name

* Phone number

* Email address

Address

* Address1

Address2

* City

* State

* Zipcode

* Country

Complaint Details

* URL of copyrighted work (where your original material is located)

* Please describe the copyrighted work so that it may be easily identified

I am the owner, or an agent authorized to act on behalf of the owner of an exclusive right that is allegedly infringed.

I have a good faith belief that the use of the material in the manner complained of is not authorized by the copyright owner, its agent, or the law.

This notification is accurate.

I acknowledge that there may be adverse legal consequences for making false or bad faith allegations of copyright infringement by using this process.

* Signature (your digital signature is legally binding)

HIGH SCHOOL

GRADUATE SCHOOL

K-8

Search 50+ Tests

math tutoring

science tutoring

foreign languages

elementary tutoring

other

Search 350+ Subjects

ACT Math : Quadrilaterals

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #302 : Act Math

Example Question #1 : How To Find The Length Of The Side Of A Trapezoid

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

Example Question #1 : Parallelograms

Example Question #1 : Parallelograms

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

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

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

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

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

All ACT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: