GMAT Math : DSQ: Calculating an angle in a polygon

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 #3 : Polygons

How many sides does a regular polygon have?

1) Each of the angles measures 140 degrees.

2) Each of the sides has measure 8.

Possible Answers:

BOTH statements TOGETHER are NOT sufficient to answer the question.

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

EITHER Statement 1 or Statement 2 ALONE is 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 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is not sufficient.

Correct answer:

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

Explanation:

The relationship between the number of sides of a regular polygon and the measure of a single angle is

$A = \frac{180(n-2)}{n}$

If we are given that A = 140 , then we can substitute and solve for :

$140 = \frac{180(n-2)}{n}$

$140 = \frac{180n-360}{n}$

140n = 180n-360

(140-180)n = -360

-40n = -360

n = 9

making the figure a nine-sided polygon.

Knowing only the measure of each side is neither necessary nor helpful; for example, it is possible to construct an equilateral triangle with sidelength 8 or a square with sidelength 8.

The correct answer is that Statement 1 alone is sufficient to answer the question, but not Statement 2 alone.

Report an Error

Example Question #4 : Polygons

Polygons_2

Note: Figure NOT drawn to scale.

Is the pentagon in the diagram above a regular pentagon?

Statement 1: $m \angle 1= 70^{\circ }$

Statement 2: The hexagon in the diagram is not a regular hexagon.

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.

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.

Correct answer:

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

Explanation:

Information about the hexagon is irrelevant, so Statement 2 has no bearing on the answer to the question.

The measures of the exterior angles of any pentagon, one per vertex, total $360^{\circ }$ , and they are congruent if the pentagon is regular, so if this is the case, each would measure $360 \div 5 = 72^{\circ }$ . But if Statement 1 is true, then an exterior angle of the pentagon measures $70^{\circ}$ . Therefore, Statement 1 is enough to answer the question in the negative.

Report an Error

Example Question #1 : Dsq: Calculating An Angle In A Polygon

What is the sum of six numbers, a,b,c,d,e,f ?

Statement 1: a,b,c,d,e,f are the measures of the interior angles of a hexagon.

Statement 2: The median of the data set $\left \{}a,b,c,d,e,f \right \}$ is 120.

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:

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

Explanation:

The sum of the measures of the six interior angles of any hexagon is 180 (6-2) = 720 , so if Statement 1 is true, then the sum of the six numbers is 720, regardless of the individual values.

Statement 2 is not enough, however, for us to deduce this sum; this only tells us the mean of the third- and fourth-highest values.

Report an Error

Example Question #1 : Dsq: Calculating An Angle In A Polygon

What is the sum of five numbers, a,b,c,d,e ?

Statement 1: a,b,c,d,e are the measures of the interior angles of a pentagon.

Statement 2: The mean of the data set $\left \{}a,b,c,d,e\right \}$ is 108.

Possible Answers:

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

Correct answer:

EITHER statement ALONE is sufficient to answer the question.

Explanation:

The sum of the measures of the five interior angles of any pentagon is 180 (5-2) = 540 , so if Statement 1 is true, then the sum of the five numbers is 540, regardless of the individual values.

The mean of five data values multiplied by 5 is the sum of the values, so if Statement 2 is true, then their sum is $108 \cdot 5 = 540$ .

Report an Error

Example Question #2 : Dsq: Calculating An Angle In A Polygon

What is the measure of an interior angle of a regular polygon?

Statement 1: The polygon has 20 sides.

Statement 2: An exterior angle of the polygon measures $18^{\circ}$ .

Possible Answers:

EITHER statement ALONE is sufficient to answer the question.

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.

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:

From Statement 1, you can calculate the measure of an interior angle as follows:

$\frac{180(20-2) }{20} = \frac{180(18) }{20} = 162 ^{\circ }$

From Statement 2, since an interior angle and an exterior angle at the same vertex form a linear pair, they are supplementary, so you can subtract 18 from 180:

$180 - 18 = 162^{\circ }$

Report an Error

Example Question #3 : Dsq: Calculating An Angle In A Polygon

Is $\textrm{ polygon } ABCDE$ a regular pentagon?

Statement 1: $m \angle A > m \angle B$

Statement 2: CD > DE

Possible Answers:

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 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.

Correct answer:

EITHER statement ALONE is sufficient to answer the question.

Explanation:

All of the interior angles of a regular polygon are congruent, as are all of its sides. Statement 1 violates the former condition; statement 2 violates the latter.

Report an Error

Example Question #4 : Dsq: Calculating An Angle In A Polygon

Thing

Note: Figure NOT drawn to scale.

The diagram above shows a triangle and a rhombus sharing a side. Is that rhombus a square?

Statement 1: The triangle is not equilateral.

Statement 2: $m \angle AVC = 150^{\circ }$

Possible Answers:

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.

BOTH statements TOGETHER are insufficient to answer the question.

Correct answer:

BOTH statements TOGETHER are insufficient to answer the question.

Explanation:

To show that the rhombus is a square, you need to demonstrate that one of its angles is a right angle - that is, $90 ^{\circ }$ . Both statements together are insufficent - if $m \angle AVC = 150^{\circ }$ , you would need to demonstrate that $m \angle AVD = 60^{\circ }$ is true or false, and the fact that the triangle is not equilateral is not enough to prove or to disprove this.

Report an Error

Example Question #6 : Dsq: Calculating An Angle In A Polygon

Hexagon

Note: Figure NOT drawn to scale.

$m \angle A = m \angle C = m \angle E = 119$

What is $m \angle D$ ?

Statement 1: $m \angle B$ , $m \angle D$ , and $m \angle F$ are the first three terms, in order, of an arithmetic sequence.

Statement 2: $m \angle B + 2 = m \angle F$

Possible Answers:

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.

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.

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:

The sum of the measures of the angles of a hexagon is $180 (6-2) = 720^{\circ }$

Therefore,

$m \angle A + m \angle B + m \angle C + m \angle D + m \angle E + m \angle F = 720$

$\ 119 + m \angle B + 119 + m \angle D + 119 + m \angle F = 720$

$m \angle B + m \angle D + m \angle F + 357 = 720$

$m \angle B + m \angle D + m \angle F = 720 - 357 = 363$

Suppose we only know that $m \angle B$ , $m \angle D$ , and $m \angle F$ are the first three terms of an arithmetic sequence, in order. Then for some common difference ,

$m \angle B = m \angle D - d$

$\ m \angle F = m \angle D + d$

$\ \left (m \angle D - d \right )+ m \angle D \left + ( m \angle D +d \right ) = 363$

$\ 3 \cdot m \angle D \left = 363$

$m \angle D \left = 121$

Suppose we only know that $m \angle B + 2 = m \angle F$ . Then

$m \angle B + m \angle D + \left (m \angle B + 2 \right ) = 363$

$2 \cdot m \angle B + m \angle D + 2 = 363$

$2 \cdot m \angle B + m \angle D = 361$

With no further information, we cannot determine $m \angle D$ .

Report an Error

Example Question #7 : Dsq: Calculating An Angle In A Polygon

Is the degree measure of an exterior angle of a regular polygon an integer?

Statement 1: The number of sides of the polygon is a factor of 30.

Statement 2: The number of sides of the polygon is a factor of 40.

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.

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:

EITHER statement ALONE is sufficient to answer the question.

Explanation:

The sum of the degree measures of the exterior angles, one per vertex, of any polygon is 360, so each exterior angle of a regular polygon with sides measures $\frac{360}{N}$ . Therefore, the measure of one exterior angle of a regular polygon is an integer if and only if is a factor of 360.

If is a factor of a factor of 360, however, then is a factor of 360. 30 and 40 are both factors of 360: $360 \div 30 = 12$ and $360 \div 40 = 9$ . Therefore, it follows from either statement that the number of sides is a factor of 360, and each exterior angle has a degree measure that is an integer.

Report an Error

Example Question #8 : Dsq: Calculating An Angle In A Polygon

Is the degree measure of an exterior angle of a regular polygon an integer?

Statement 1: The number of sides of the polygon is divisible by 7.

Statement 2: The number of sides of the polygon is divisible by 10.

Possible Answers:

EITHER statement ALONE is sufficient to answer the question.

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 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:

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

Explanation:

The sum of the degree measures of the exterior angles, one per vertex, of any polygon is 360, so each exterior angle of a regular polygon with sides measures $\frac{360}{N}$ .

For $\frac{360}{N}$ to be an integer, every factor of must be a factor of 360. This does not happen if 7 is a factor of , so Statement 1 disproves this. This may or may not happen if 10 is a factor of - $\frac{360}{40} = 9$ , but $\frac{360}{80} = 4.5$ , so Statement 2 does not provide an answer.

Report an Error

All GMAT Math Resources

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

Popular Subjects

Algebra Tutors in Seattle, ACT Tutors in Los Angeles, Biology Tutors in Washington DC, Chemistry Tutors in Seattle, ISEE Tutors in Seattle, Physics Tutors in Washington DC, MCAT Tutors in Philadelphia, Calculus Tutors in New York City, Reading Tutors in Philadelphia, MCAT Tutors in Los Angeles

Popular Courses & Classes

GMAT Courses & Classes in Miami, GRE Courses & Classes in Los Angeles, MCAT Courses & Classes in Philadelphia, GRE Courses & Classes in Miami, GRE Courses & Classes in San Diego, SSAT Courses & Classes in Boston, LSAT Courses & Classes in San Diego, SAT Courses & Classes in San Diego, LSAT Courses & Classes in Washington DC, SSAT Courses & Classes in Seattle

Popular Test Prep

SSAT Test Prep in Washington DC, SAT Test Prep in Miami, MCAT Test Prep in San Diego, MCAT Test Prep in New York City, SAT Test Prep in Atlanta, SAT Test Prep in San Diego, GRE Test Prep in Chicago, GRE Test Prep in Miami, GMAT Test Prep in Seattle, GMAT 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)

Email address:
Your name:
Feedback:

GMAT Math : DSQ: Calculating an angle in a polygon

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #3 : Polygons

Example Question #4 : Polygons

Example Question #1 : Dsq: Calculating An Angle In A Polygon

Example Question #1 : Dsq: Calculating An Angle In A Polygon

Example Question #2 : Dsq: Calculating An Angle In A Polygon

Example Question #3 : Dsq: Calculating An Angle In A Polygon

Example Question #4 : Dsq: Calculating An Angle In A Polygon

Example Question #6 : Dsq: Calculating An Angle In A Polygon

Example Question #7 : Dsq: Calculating An Angle In A Polygon

Example Question #8 : Dsq: Calculating An Angle In A Polygon

All GMAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details