GMAT Math : Intersecting Angles and Lines

Study concepts, example questions & explanations for GMAT Math

Create An Account

All GMAT Math Resources

22 Diagnostic Tests 693 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Dsq: Calculating The Angle Of An Intersection

Lines

Note: Figure NOT drawn to scale.

Refer to the above diagram. Evaluate .

Statement 1: x= 2v

Statement 2: y= 2x

Possible Answers:

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

BOTH statements TOGETHER are insufficient to answer the question.

EITHER statement ALONE is sufficient to answer the question.

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

Correct answer:

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

Explanation:

Statement 1 alone gives insufficient information. It only gives a relationship between and , but no further clues about the measures of any angle are given.

Statement 2 alone gives insufficient information; w = y = 2x , since the angles with those measures are vertical; since no measures are known, cannot be calculated.

Now assume both statements are true. Again, from Statement 1, x = 2v ; from Statement 2, y = 2x= 2(2v)= 4v . Again, from the diagram, w = y = 4v . Three angles with measures x,v,w together form a straight angle, so

x+v+w = 180

2v+v+4v = 180

7v = 180

$v = 180 \div 7 = 25 \frac{5}{7}$

$w = 4v = 4 \cdot 25\frac{5}{7} = 102 \frac{6}{7}$

Therefore, both statements together are sufficient to answer the question.

Report an Error

Example Question #2 : Dsq: Calculating The Angle Of An Intersection

Lines

Note: Figure NOT drawn to scale.

Refer to the above diagram. Evaluate .

Statement 1: x+ y = 150

Statement 2: w+v = 130

Possible Answers:

BOTH statements TOGETHER are insufficient to answer the question.

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

EITHER statement ALONE is sufficient to answer the question.

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

Correct answer:

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

Explanation:

Assume Statement 1 alone. From the diagram, the three angles of measure x,y,v together form a straight angle, so

x+y+v= 180

From Statement 1,

x+ y = 150 ,

so by the subtraction property of equality,

x+y+v- (x+y)= 180 -150

v= 30

Assume Statement 2 alone. w+v = 130 , but there is no clue about the value of or any other angle measure, so the value of cannot be computed.

Report an Error

Example Question #1 : Intersecting Angles And Lines

Transversal

Note: Figure NOT drawn to scale. Do not assume lines are parallel or perpendicular simply by appearance.

Evaluate $m \angle 1$ .

Statement 1: $m \angle 4 = 88^{\circ}$

Statement 2: $m \angle 8 = 88^{\circ }$

Possible Answers:

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

EITHER statement ALONE is sufficient to answer the question.

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

BOTH statements TOGETHER are insufficient to answer the question.

Correct answer:

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

Explanation:

Assume Statement 1 alone. $\angle 1$ and $\angle 4$ are vertical angles, so they must have the same measure; $m \angle 1 =m \angle 4 = 88^{\circ}$ .

Assume Statement 2 alone. $\angle 1$ and $\angle 8$ are alternating exterior angles, which are congruent if and only if l || m ; however, we do not know whether l || m , so no conclusions can be made about $m \angle 1$ .

Report an Error

Example Question #2 : Intersecting Angles And Lines

Lines

Note: Figure NOT drawn to scale.

Refer to the above diagram. Evaluate .

Statement 1: x+v = 74

Statement 2: z+y+x+v= 254

Possible Answers:

BOTH statements TOGETHER are insufficient to answer the question.

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

EITHER statement ALONE is sufficient to answer the question.

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

Correct answer:

EITHER statement ALONE is sufficient to answer the question.

Explanation:

Assume Statement 1 alone. x+v+y = 180 , since the three angles of these measures together form a straight angle. Also, from Statement 1, x+v = 74 . Therefore:

x+v+y = 180

x+v+y - (x+v) = 180- 74

y = 106

Assume Statement 2 alone. Again, x+v+y = 180 , and from Statement 2, z+y+x+v= 254 . Therefore,

z+y+x+v= 254

z+y+x+v - (x+y+v)= 254- 180

z= 74

Since the angles of measures and form a linear pair, they are supplementary, and y = 180-z = 180 - 74 = 106 .

Report an Error

Example Question #1 : Dsq: Calculating The Angle Of An Intersection

Lines

Note: Figure NOT drawn to scale.

Refer to the above diagram. Evaluate .

Statement 1: x+y = w+v

Statement 2: z= 2x

Possible Answers:

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

EITHER statement ALONE is sufficient to answer the question.

BOTH statements TOGETHER are insufficient to answer the question.

Correct answer:

BOTH statements TOGETHER are insufficient to answer the question.

Explanation:

We show that both statements together give insufficient information. Assume both statements together. Consider the following two cases:

Case 1: z= 80

Since the angles of measures and form linear pairs with the angle of measure , each is supplementary to that angle and, subsequently, w=y=180 - z = 180 - 80 = 100 .

The angle of measure x+v is vertical to the angle of measure , so the two must be congruent; x+v =z= 80 .

From Statement 1,

x+y = w+v

x+100 = 100+v

x=v

Since x+v = 80 and x=v , then x=v = 40 .

These values are therefore consistent with the diagram and with both statements.

Case 2: z= 70

We can find the values of the other variables as before:

w=y=180 - z = 180 - 70 = 110

x+v =z= 70

x=v , so x=v = 35 .

Again, all values are consistent with the diagram and both statements.

Since at least two different values of satify the conditions, the two statements are insufficient.

Report an Error

Example Question #6 : Dsq: Calculating The Angle Of An Intersection

Transversal

Note: Figure NOT drawn to scale. Do not assume lines are parallel or perpendicular simply by appearance.

Evaluate $m \angle 1$ .

Statement 1: l || m

Statement 2: $t \perp m$

Possible Answers:

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

EITHER statement ALONE is sufficient to answer the question.

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

BOTH statements TOGETHER are insufficient to answer the question.

Correct answer:

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

Explanation:

Statement 1 alone gives us that l || m , but reveals no clues about any of the eight angle measures. From Statement 2 alone, that $t \perp m$ , we can assume that $\angle 5, \angle 6, \angle 7$ , and $\angle 8$ all have measure $90 ^{\circ }$ , but no clues are given about any of the other four angles—in particular, $\angle 1$ .

Assume both statements are true. From Statement 1, l || m , and by way of the Parallel Postulate, corresponding angles have the same measure—in particular, $m \angle 1 = m \angle 5$ . From Statement 2, we know that $m \angle 5= 90^{\circ }$ . From these two statements, $m \angle 1= 90^{\circ }$ .

Report an Error

Example Question #5 : Dsq: Calculating The Angle Of An Intersection

Chord

Note: Figure NOT drawn to scale.

Give the measure of $\angle CMD$ in the above diagram.

Statement 1: $\widehat{AB}$ is an arc of measure $30^{\circ }$ .

Statement 2: $\widehat{CD}$ is an arc of measure $44 ^{\circ }$ .

Possible Answers:

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

EITHER statement ALONE is sufficient to answer the question.

BOTH statements TOGETHER are insufficient to answer the question.

Correct answer:

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

Explanation:

If two chords of a circle intersect inside it, then the measure of an angle formed is equal to the arithmetic mean of the measures of arc it intercepts and the arc its vertical angle intercepts. In other words, in this diagram,

$m \angle CMD = \frac{m\widehat{AB} + m\widehat{CD}}{2}$

Both arc measures are needed to find the measure of the angle. Neither statement alone give both; the two together do.

Report an Error

All GMAT Math Resources

22 Diagnostic Tests 693 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

GMAT Tutors in Chicago, GMAT Tutors in Philadelphia, SAT Tutors in Seattle, SSAT Tutors in Chicago, GMAT Tutors in Dallas Fort Worth, English Tutors in Denver, Math Tutors in Houston, English Tutors in Miami, SAT Tutors in Los Angeles, Computer Science Tutors in Chicago

Popular Courses & Classes

SAT Courses & Classes in New York City, MCAT Courses & Classes in Boston, GMAT Courses & Classes in Seattle, SAT Courses & Classes in Seattle, ISEE Courses & Classes in Boston, ISEE Courses & Classes in Miami, LSAT Courses & Classes in Phoenix, GRE Courses & Classes in Houston, LSAT Courses & Classes in Houston, ACT Courses & Classes in Seattle

Popular Test Prep

SAT Test Prep in San Diego, ACT Test Prep in Dallas Fort Worth, MCAT Test Prep in Atlanta, ISEE Test Prep in Washington DC, SAT Test Prep in Chicago, SAT Test Prep in Boston, MCAT Test Prep in Houston, ISEE Test Prep in Los Angeles, GMAT Test Prep in Houston, SAT Test Prep in New York City

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)

Email address:
Your name:
Feedback:

GMAT Math : Intersecting Angles and Lines

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #1 : Dsq: Calculating The Angle Of An Intersection

Example Question #2 : Dsq: Calculating The Angle Of An Intersection

Example Question #1 : Intersecting Angles And Lines

Example Question #2 : Intersecting Angles And Lines

Example Question #1 : Dsq: Calculating The Angle Of An Intersection

Example Question #6 : Dsq: Calculating The Angle Of An Intersection

Example Question #5 : Dsq: Calculating The Angle Of An Intersection

All GMAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details