We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

ACT Math : How to find an angle in a quadrilateral

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 #1 : How To Find An Angle In A Quadrilateral

$\angle ADB$ bisects $\overline{EC}$ . If $\angle DAB=35$ then, in degrees, what is the value of $\angle ADB$ ?

Possible Answers:

$55^\circ$

$70^\circ$

$110^\circ$

$145^\circ$

$125^\circ$

Correct answer:

$110^\circ$

Explanation:

A rectangle has two sets of parallel sides with all angles equaling 90 degrees.

Since $\angle ADB$ bisects $\overline{EC}$ into two equal parts, this creates an isosceles triangle ABD .

Therefore $\angle DAB = \angle DBA$ . The sum of the angles in a triangle is 180 degrees.

Therefore $\angle ADB = 180-35-35 = 110$

Report an Error

Example Question #431 : Plane Geometry

The rhombus above is bisected by two diagonals.

If $\angle ADE = x+35$ and $\angle EAB = 2x+10$ then, in degrees, what is the value of the $\angle BCD$ ?

Note: The shape above may not be drawn to scale.

Possible Answers:

$15^\circ$

$90^\circ$

$50^\circ$

$100^\circ$

$80^\circ$

Correct answer:

$80^\circ$

Explanation:

A rhombus is a quadrilateral with two sets of parallel sides as well as equal opposite angles. Since the lines drawn inside the rhombus are diagonals, $\angle DAB,\angle ABC,\angle BCD,$ and $\angle CDA$ are each bisected into two equal angles.

Therefore, $\angle ADE=\angle ABE$ , which creates a triangle in the upper right quadrant of the kite. The sum of angles in a triangle is 180 degreees.

Thus,

180 = (x+35)+(2x+10)+90=3x+135

3x=45

x=15

$\angle EAB = 2(15)+10=40$

Since $\angle EAB$ is only half of $\angle DAB$ ,

$\angle DAB=2(40)=80$

$\angle DAB=\angle BCD=80$

Report an Error

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

Q10

If $\angle A = 15+2y$ and $\angle C=\frac{y+96}{2}$ , then, in degrees, what is the value of $\angle B$ ?

Note: The figure may not be drawn to scale.

Possible Answers:

$118^\circ$

$124^\circ$

$132^\circ$

$121^\circ$

$126^\circ$

Correct answer:

$121^\circ$

Explanation:

In a rhombus, opposite angles are equal to each other. Therefore we can set $\angle A$ and $\angle C$ equal to one another and solve for :

$15+2y=\frac{y+96}{2}$

30+4y=y+96

3y=66

$y=\frac{66}{3}=22$

Therefore, $\angle A = \angle C=59$

A rhombus, like any other quadrilateral, has a sum of angles of 360 degrees.

$\angle B = \frac{360-59-59}{2}=121$

Report an Error

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

The interior angles of a quadrilateral are $71^{\circ}$ , $9x^{\circ}$ , $5x^{\circ}$ , and $3x^{\circ}$ . What is the measure of the smallest angle of the quadrilateral?

Possible Answers:

$\small 34^{o}$

$\small 20^{o}$

$\small 71^{o}$

$\small 30^o$

$\small 51^{o}$

Correct answer:

$\small 51^{o}$

Explanation:

In order to solve this problem we need the following key piece of knowledge: the interior angles of a quadrilateral add up to 360 degrees. Now, we can write the following equation:

71+9x+5x+3x=360

When we combine like terms, we get the following:

71+17x=360

We will need to subtract 71 from both sides of the equation:

71-71+17x=360-71

17x=289

Now, we will divide both sides of the equation by 17.

$\frac{17x}{17}=\frac{289}{17}$

x=17

We now have a value for the x-variable; however, the problem is not finished. The question asks for the measure of the smallest angle. We know that the smallest angle will be one of the following:

$71^{\circ}$ or $3x^{\circ}$

In order to find out, we will substitute 17 degrees for the x-variable.

$3(17^{\circ})=51^{\circ}$

Because 51 degrees is less than 71 degrees, the measure of the smallest angle is the following:

$51^{\circ}$

Report an Error

View ACT Math Tutors

Barry
Certified Tutor

State University of New York at Binghamton, Master of Science, Economics.

View ACT Math Tutors

Pushpendra
Certified Tutor

university of allahabad, Bachelor of Science, Mathematics.

View ACT Math Tutors

Godswill
Certified Tutor

Rivers State University, Bachelor of Engineering, Mechanical Engineering. Texas Southern University, Master of Science, Compu...

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

MCAT Courses & Classes in San Francisco-Bay Area, MCAT Courses & Classes in San Diego, SSAT Courses & Classes in Boston, ACT Courses & Classes in Boston, SAT Courses & Classes in Los Angeles, SAT Courses & Classes in Atlanta, Spanish Courses & Classes in San Diego, SAT Courses & Classes in New York City, SAT Courses & Classes in Miami, SSAT Courses & Classes in Chicago

Popular Test Prep

SAT Test Prep in Phoenix, SAT Test Prep in Dallas Fort Worth, GMAT Test Prep in Seattle, LSAT Test Prep in Boston, SSAT Test Prep in Seattle, GRE Test Prep in Boston, ISEE Test Prep in Dallas Fort Worth, ISEE Test Prep in New York City, MCAT Test Prep in Los Angeles, LSAT Test Prep in Chicago

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 : How to find an angle in a quadrilateral

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

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

Example Question #431 : Plane Geometry

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

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

All ACT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: