Call Now to Set Up Tutoring:

(888) 888-0446

ISEE Upper Level Math : How to find an angle

Study concepts, example questions & explanations for ISEE Upper Level Math

Create An Account

All ISEE Upper Level Math Resources

6 Diagnostic Tests 244 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

← Previous 1 2 Next →

Example Question #1 : How To Find An Angle

Lines

Examine the above diagram. If $l \parallel m$ , give in terms of .

Possible Answers:

165 +x

75-x

75 + x

165-x

131 -x

Correct answer:

165-x

Explanation:

The two marked angles are same-side exterior angles of parallel lines, which are supplementary - that is, their measures have sum 180. We can solve for in this equation:

(y-17) + (x + 32) = 180

y + x-17 + 32= 180

y + x+15= 180

y + x+15- 15 - x = 180- 15 - x

y = 165- x

Report an Error

Example Question #251 : Geometry

Lines

Examine the above diagram. If $l \parallel m$ , give in terms of .

Possible Answers:

$92 - \frac{1}{2}x$

$184 - \frac{1}{2}x$

$47 - \frac{1}{2}x$

92 - x

47 - x

Correct answer:

$92 - \frac{1}{2}x$

Explanation:

The two marked angles are same-side interior angles of parallel lines, which are supplementary - that is, their measures have sum 180. We can solve for in this equation:

(2y + 15) + (x - 19) = 180

2y + x+ 15 - 19 = 180

2y + x-4 = 180

2y + x-4+4 -x = 180+4 -x

2y = 184 -x

$2y \div 2 = \left ( 184 -x \right )\div 2$

$y= 92 - \frac{1}{2}x$

Report an Error

Example Question #31 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Lines

Examine the above diagram. What is x + y ?

Possible Answers:

112

Correct answer:

Explanation:

By angle addition,

$\left ( x - 13\right )+ 100 + (y + 25) = 180$

$x - 13\right+ 100 + y + 25 = 180$

$x + y - 13\right+ 100+ 25 = 180$

x + y +112 = 180

x + y +112 - 112= 180- 112

x + y = 68

Report an Error

Example Question #4 : How To Find An Angle

Lines

Examine the above diagram. Which of the following statements must be true whether or not and are parallel?

Possible Answers:

$m \angle 1 + m \angle 6 = 180 ^{\circ }$

$\angle 2 \cong \angle 6$

$m \angle 4 + m \angle 7 = 180 ^{\circ }$

$\angle 5 \cong \angle 8$

$\angle 5 \cong \angle 4$

Correct answer:

$\angle 5 \cong \angle 8$

Explanation:

Four statements can be eliminated by the various parallel theorems and postulates. Congruence of alternate interior angles or corresponding angles forces the lines to be parallel, so

$\angle 5 \cong \angle 4 \Rightarrow l \parallel m$ and

$\angle 2 \cong \angle 6 \Rightarrow l \parallel m$ .

Also, if same-side interior angles or same-side exterior angles are supplementary, the lines are parallel, so

$m \angle 4 + m \angle 7 = 180 ^{\circ } \Rightarrow l \parallel m$ and

$m \angle 1 + m \angle 6 = 180 ^{\circ } \Rightarrow l \parallel m$ .

However, $\angle 5 \cong \angle 8$ whether or not $l \parallel m$ since they are vertical angles, which are always congruent.

Report an Error

Example Question #1 : How To Find An Angle

$\angle 1$ and $\angle 2$ are supplementary; $\angle 1$ and $\angle 3$ are complementary.

$m \angle 2 = 100 ^{\circ }$ .

What is $m \angle 3$ ?

Possible Answers:

$50^{\circ }$

$80^{\circ }$

$100^{\circ }$

$10^{\circ }$

Correct answer:

$10^{\circ }$

Explanation:

Supplementary angles and complementary angles have measures totaling $180^{\circ }$ and $90^{\circ }$ , respectively.

$m \angle 2 = 100 ^{\circ }$ , so its supplement $\angle 1$ has measure

$m \angle 1 = 180^{\circ } - m \angle 2 = 180^{\circ } - 100 ^{\circ } = 80^{\circ }$

$\angle 3$ , the complement of $\angle 1$ , has measure

$m \angle 3 = 90^{\circ } - m \angle 1 = 90^{\circ } - 80 ^{\circ } = 10^{\circ }$

Report an Error

Example Question #6 : How To Find An Angle

Thingy

Note: Figure NOT drawn to scale.

In the above figure, $m \angle 1=\left ( x+17 \right )^{\circ}$ and $m \angle 2= \left (7x+11 \right )^{\circ}$ . Which of the following is equal to $m \angle 1$ ?

Possible Answers:

$36^{\circ}$

$26^{\circ}$

$7\frac{3}{4}^{\circ }$

$21\frac{5}{7}^{\circ}$

$29\frac{5}{7}^{\circ}$

Correct answer:

$36^{\circ}$

Explanation:

$\angle 1$ and $\angle 2$ form a linear pair, so their angle measures total $180^{\circ}$ . Set up and solve the following equation:

$m \angle 1+ m \angle 2 = 180^{\circ}$

$\left ( x+17 \right ) + \left (7x+11 \right ) = 180$

8x+28 = 180

8x=152

x = 19

$m \angle 1=\left ( x+17 \right )^{\circ} = \left ( 19+17 \right )^{\circ} = 36^{\circ}$

Report an Error

Example Question #261 : Geometry

Two angles which form a linear pair have measures $(2x+72)^{\circ}$ and $(5x-125)^{\circ}$ . Which is the lesser of the measures (or the common measure) of the two angles?

Possible Answers:

$81\frac{1}{2} ^{\circ }$

$22\frac{6}{7}^{\circ}$

$33\frac{2}{7}^{\circ }$

$65\frac{2}{3 } ^{\circ }$

$41\frac{3}{7}^{\circ}$

Correct answer:

$41\frac{3}{7}^{\circ}$

Explanation:

Two angles that form a linear pair are supplementary - that is, they have measures that total $180^{\circ}$ . Therefore, we set and solve for in this equation:

(2x+72)+(5x-125)= 180

7x - 53 = 180

7x = 233

$x = \frac{233}{7}= 33 \frac{2}{7}$

The two angles have measure

$2 \cdot 33 \frac{2}{7} +72= 138 \frac{4}{7} ^{\circ}$

and

$5 \cdot 33 \frac{2}{7} -125 = 41\frac{3}{7}^{\circ}$

$41\frac{3}{7}^{\circ}$ is the lesser of the two measures and is the correct choice.

Report an Error

Example Question #261 : Geometry

Two vertical angles have measures $(3x+14)^{\circ }$ and $\left ( 5x-17\right )^{\circ }$ . Which is the lesser of the measures (or the common measure) of the two angles?

Possible Answers:

$15\frac{1}{2}^{\circ }$

$22\frac{7}{8}^{\circ}$

$60\frac{1}{2} ^{\circ }$

$68\frac{5}{8}^{\circ}$

$41\frac{1}{8}^{\circ}$

Correct answer:

$60\frac{1}{2} ^{\circ }$

Explanation:

Two vertical angles - angles which share a vertex and whose union is a pair of lines - have the same measure. Therefore, we set up and solve the equation

3x+14= 5x-17

14= 2x-17

2x= 31

$x= 15\frac{1}{2}$

$3x+14 = 3 \cdot 15\frac{1}{2} + 14 = 46\frac{1}{2} + 14= 60\frac{1}{2} ^{\circ }$

Report an Error

Example Question #9 : How To Find An Angle

A line intersects parallel lines and . $\angle 1$ and $\angle 2$ are corresponding angles; $\angle 1$ and $\angle 3$ are same side interior angles.

$m \angle 1 = \left (3x+2y \right )^{\circ }$

$m \angle 2 = \left ( 4x+21\right )^{\circ }$

$m \angle 3 = \left ( 2y-27\right )^{\circ}$

Evaluate x+y .

Possible Answers:

x+y = 120

x+y = 60

x+y = 30

x+y = 45

x+y = 90

Correct answer:

x+y = 60

Explanation:

When a transversal such as crosses two parallel lines, two corresponding angles - angles in the same relative position to their respective lines - are congruent. Therefore,

3x+2y = 4x+21

3x+2y- 3x - 21 = 4x+21 - 3x - 21

x = 2y - 21

Two same-side interior angles are supplementary - that is, their angle measures total 180 - so

3x+2y + 2y-27 = 180

3x+4y-27 = 180

3x+4y= 207

We can solve this system by the substitution method as follows:

3( 2y - 21)+4y= 207

6y-63+4y= 207

10y-63= 207

10y = 270

y = 27

Backsolve:

x = 2y - 21

x = 2 (27)- 21 = 54-21 = 33

x+y = 27+33 = 60 , which is the correct response.

Report an Error

Example Question #1 : How To Find An Angle

Vertical_angles

Note: Figure NOT drawn to scale.

Refer to the above diagram. Give the measure of $\angle 1$ .

Possible Answers:

$88^{\circ }$

$128^{\circ }$

$144^{\circ }$

$96^{\circ }$

$120 ^{\circ }$

Correct answer:

$120 ^{\circ }$

Explanation:

The top and bottom angles, being vertical angles - angles which share a vertex and whose union is a pair of lines - have the same measure, so

2x+y = 2y ,

or, simplified,

2x+y - y= 2y - y

y = 2x

The right and bottom angles form a linear pair, so their degree measures total 180. That is,

2y+ 8x = 180

Substitute for :

2(2x)+ 8x = 180

4x+8x = 180

12x= 180

x = 15

The left and right angles, being vertical angles, have the same measure, so, since the right angle measures $\left (8x \right )^{\circ } =\left (8 \cdot 15 \right )^{\circ } = 120 ^{\circ }$ , this is also the measure of the left angle, $\angle 1$ .

Report an Error

← Previous 1 2 Next →

View Tutors

Jennifer
Certified Tutor

McKendree University, Bachelor in Business Administration, Accounting and Business Management. Lindenwood University, Masters...

View Tutors

Matt
Certified Tutor

View Tutors

Brandee
Certified Tutor

Western Governors University, Bachelor of Science, Mathematics Teacher Education.

All ISEE Upper Level Math Resources

6 Diagnostic Tests 244 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Chemistry Tutors in Washington DC, GMAT Tutors in Denver, Spanish Tutors in Seattle, Math Tutors in New York City, MCAT Tutors in San Francisco-Bay Area, Spanish Tutors in San Diego, Physics Tutors in Dallas Fort Worth, GRE Tutors in New York City, Biology Tutors in Miami, Computer Science Tutors in San Francisco-Bay Area

Popular Courses & Classes

SSAT Courses & Classes in Seattle, Spanish Courses & Classes in San Francisco-Bay Area, SSAT Courses & Classes in Chicago, LSAT Courses & Classes in San Diego, Spanish Courses & Classes in San Diego, Spanish Courses & Classes in Chicago, ACT Courses & Classes in Phoenix, GMAT Courses & Classes in Miami, SSAT Courses & Classes in San Francisco-Bay Area, LSAT Courses & Classes in Seattle

Popular Test Prep

SAT Test Prep in Dallas Fort Worth, ISEE Test Prep in New York City, SSAT Test Prep in Denver, ACT Test Prep in Los Angeles, MCAT Test Prep in Phoenix, GRE Test Prep in New York City, SSAT Test Prep in Atlanta, SSAT Test Prep in Phoenix, LSAT Test Prep in Atlanta, ACT Test Prep in Miami

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

ISEE Upper Level Math : How to find an angle

Study concepts, example questions & explanations for ISEE Upper Level Math

All ISEE Upper Level Math Resources

Example Questions

Example Question #1 : How To Find An Angle

Example Question #251 : Geometry

Example Question #31 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Example Question #4 : How To Find An Angle

Example Question #1 : How To Find An Angle

Example Question #6 : How To Find An Angle

Example Question #261 : Geometry

Example Question #261 : Geometry

Example Question #9 : How To Find An Angle

Example Question #1 : How To Find An Angle

All ISEE Upper Level Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: