Call Now to Set Up Tutoring:

(888) 888-0446

High School Math : Geometry

Study concepts, example questions & explanations for High School Math

Create An Account

All High School Math Resources

8 Diagnostic Tests 613 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : How To Find An Angle In An Acute / Obtuse Triangle

In a given triangle, the angles are in a ratio of 1:3:5. What size is the middle angle?

Possible Answers:

$45^{\circ}$

$60^{\circ}$

$20^{\circ}$

$75^{\circ}$

$90^{\circ}$

Correct answer:

$60^{\circ}$

Explanation:

Since the sum of the angles of a triangle is $180^{\circ}$ , and given that the angles are in a ratio of 1:3:5, let the measure of the smallest angle be , then the following expression could be written:

$x+3x+5x=180$

$9x=180$

$x=20$

If the smallest angle is 20 degrees, then given that the middle angle is in ratio of 1:3, the middle angle would be 3 times as large, or 60 degrees.

Report an Error

Example Question #431 : Psat Mathematics

Triangle ABC has angle measures as follows:

$\dpi{100} \small m\angle ABC=4x+3$

$\dpi{100} \small m\angle ACB=2x+6$

$\dpi{100} \small m\angle BAC=3x$

What is $\dpi{100} \small m\angle BAC$ ?

Possible Answers:

Correct answer:

Explanation:

The sum of the measures of the angles of a triangle is 180.

Thus we set up the equation $\dpi{100} \small 4x+3+2x+6+3x=180$

After combining like terms and cancelling, we have $\dpi{100} \small 9x=171\rightarrow x=19$

Thus $\dpi{100} \small m\angle BAC=3x=57$

Report an Error

Example Question #431 : Psat Mathematics

The base angle of an isosceles triangle is five more than twice the vertex angle. What is the base angle?

Possible Answers:

$55$

$47$

$62$

$73$

$34$

Correct answer:

$73$

Explanation:

Every triangle has 180 degrees. An isosceles triangle has one vertex angle and two congruent base angles.

Let $x$ = the vertex angle and $2x+5$ = the base angle

So the equation to solve becomes $x+(2x+5)+(2x+5)=180$

Thus the vertex angle is 34 and the base angles are 73.

Report an Error

Example Question #1 : How To Find An Angle In An Acute / Obtuse Triangle

The base angle of an isosceles triangle is 15 less than three times the vertex angle. What is the vertex angle?

Possible Answers:

Correct answer:

Explanation:

Every triangle contains 180 degrees. An isosceles triangle has one vertex angle and two congruent base angles.

Let = vertex angle and 3x-15 = base angle

So the equation to solve becomes x+(3x-15)+(3x-15)=180 .

Report an Error

Example Question #1 : How To Find An Angle In An Acute / Obtuse Triangle

The base angle of an isosceles triangle is ten less than twice the vertex angle. What is the vertex angle?

Possible Answers:

$70^{\circ}$

$35^{\circ}$

$40^{\circ}$

$65^{\circ}$

$20^{\circ}$

Correct answer:

$40^{\circ}$

Explanation:

Every triangle has 180 degrees. An isosceles triangle has one vertex angle and two congruent base angles.

Let = vertex angle and 2x - 10 = base angle

So the equation to solve becomes x + (2x - 10) + (2x - 10) = 180

So the vertex angle is 40 and the base angles is 70

Report an Error

Example Question #141 : Triangles

The base angle of an isosceles triangle is 10 more than twice the vertex angle. What is the vertex angle?

Possible Answers:

$32^{\circ}$

$74^{\circ}$

$60^{\circ}$

$45^{\circ}$

$50^{\circ}$

Correct answer:

$32^{\circ}$

Explanation:

Every triangle has 180 degrees. An isosceles triangle has one vertex angle and two congruent base angles.

Let = the vertex angle and 2x + 10 = the base angle

So the equation to solve becomes x + (2x +10) + (2x +10) = 180

The vertex angle is 32 degrees and the base angle is 74 degrees

Report an Error

Example Question #432 : Geometry

In an isosceles triangle, the vertex angle is 15 less than the base angle. What is the base angle?

Possible Answers:

Correct answer:

Explanation:

Every triangle has 180 degrees. An isosceles triangle has one vertex angle and two congruent base angles.

Let = base angle and x - 15 = vertex angle

So the equation to solve becomes (x - 15) + x + x = 180

Thus, 65 is the base angle and 50 is the vertex angle.

Report an Error

Example Question #11 : Isosceles Triangles

In an isosceles triangle the vertex angle is half the base angle. What is the vertex angle?

Possible Answers:

$108$

$54$

$45$

$36$

$72$

Correct answer:

$36$

Explanation:

Every triangle has 180 degrees. An isosceles triangle has one vertex angle and two congruent base angles.

Let $x$ = base angle and $0.5x$ = vertex angle

So the equation to solve becomes $x+x+0.5x=180$ , thus $x=72$ is the base angle and $0.5x=36$ is the vertex angle.

Report an Error

Example Question #1 : How To Find An Angle In An Acute / Obtuse Triangle

If the average of the measures of two angles in a triangle is 75^o, what is the measure of the third angle in this triangle?

Possible Answers:

75°

40°

30°

65°

50°

Correct answer:

30°

Explanation:

The sum of the angles in a triangle is 180^o: a + b + c = 180

In this case, the average of a and b is 75:

(a + b)/2 = 75, then multiply both sides by 2

(a + b) = 150, then substitute into first equation

150 + c = 180

c = 30

Report an Error

Example Question #231 : Plane Geometry

Which of the following can NOT be the angles of a triangle?

Possible Answers:

45, 90, 100

30, 60, 90

1, 2, 177

30.5, 40.1, 109.4

45, 45, 90

Correct answer:

45, 90, 100

Explanation:

In a triangle, there can only be one obtuse angle. Additionally, all the angle measures must add up to 180.

Report an Error

View Tutors

Alice
Certified Tutor

Bridgewater College, Bachelor in Arts, English. Longwood University, Certificate, Teacher Education, Multiple Levels.

View Tutors

Michele
Certified Tutor

University of Rome, Professional (JD, MD, DMD, etc), Law. Saint John's University -NY, Master of Science, Marketing.

View Tutors

Kayathry
Certified Tutor

All High School Math Resources

8 Diagnostic Tests 613 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

LSAT Tutors in Boston, French Tutors in Denver, ISEE Tutors in New York City, Computer Science Tutors in Dallas Fort Worth, Reading Tutors in Boston, Algebra Tutors in Atlanta, ACT Tutors in Denver, Calculus Tutors in New York City, SSAT Tutors in Seattle, English Tutors in Houston

Popular Courses & Classes

GMAT Courses & Classes in Boston, SSAT Courses & Classes in New York City, MCAT Courses & Classes in San Diego, ACT Courses & Classes in San Diego, GRE Courses & Classes in Houston, GRE Courses & Classes in Denver, MCAT Courses & Classes in Boston, GMAT Courses & Classes in Los Angeles, GRE Courses & Classes in San Diego, GRE Courses & Classes in Washington DC

Popular Test Prep

GRE Test Prep in Houston, ISEE Test Prep in San Diego, SSAT Test Prep in Washington DC, GMAT Test Prep in Phoenix, SSAT Test Prep in Dallas Fort Worth, GMAT Test Prep in Boston, GMAT Test Prep in Miami, SAT Test Prep in Miami, GRE Test Prep in Phoenix, ACT 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

High School Math : Geometry

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #1 : How To Find An Angle In An Acute / Obtuse Triangle

Example Question #431 : Psat Mathematics

Example Question #431 : Psat Mathematics

Example Question #1 : How To Find An Angle In An Acute / Obtuse Triangle

Example Question #1 : How To Find An Angle In An Acute / Obtuse Triangle

Example Question #141 : Triangles

Example Question #432 : Geometry

Example Question #11 : Isosceles Triangles

Example Question #1 : How To Find An Angle In An Acute / Obtuse Triangle

Example Question #231 : Plane Geometry

All High School Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: