BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Target Test Prep · GMAT

Choose how you want to prepare

Learn live with an expert or move at your own pace. Every option includes the complete TTP study system.

★★★★★5.0559 reviews
GMATLiveTeach Starts Oct 17
Chris Peckover, Target Test Prep GMAT expert
LIVE ONLINE CLASSES

Get Ready for GMAT Test Day Faster with Live Online Classes

with Chris Peckover, 100th-Percentile GMAT Scorer

Oct 17 · Chris Peckover
Sat · 11:00 AM to 2:00 PM ET
Oct 20 · Chris Peckover
Tue, Thu · 8:00 to 10:00 PM ET
Oct 25 · Josh Braslow
Sun · 1:00 to 4:00 PM ET
Included
40 hours of live online classes + 6 months of TTP OnDemand
  • Attend the first class for free
  • Every class is recorded, so you never fall behind
View classes & enroll
Limited seats availableTarget Test Prep
EALiveTeachOnDemand 5 seats left Start anytime
EXECUTIVE ASSESSMENT

Target Test Prep EA OnDemand

Self-paced EA prep. Study on your schedule.

Logan Thompson
EXECUTIVE ASSESSMENT

Sep 6 to Dec 6, 2026

with Logan Thompson

165+ EA score guarantee
$05-day trial no automatic billing
Schedule
Sun · 9:30 AM to 12:30 PM ET
Included
40 hours of live online classes plus six months of access to the complete TTP EA OnDemand course.
  • 165+ EA Score Guarantee
  • 4,100+ Quant, Verbal, and Integrated Reasoning practice questions
  • 400+ hours of in-depth video lessons
  • 3,000+ step-by-step video solutions
View EA class & enroll Start free 5-day trial
Limited cohort · enrollment openTrial includes full course accessTarget Test Prep
GMATOnDemand Start anytime
SELF-PACED MASTERCLASS

Target Test Prep GMAT OnDemand

Complete access from day one. Study on your schedule.

715+ score guarantee
$0to start then $127/mo
  • Personalized study plan and analytics
  • Thousands of lessons and practice questions
Start free 5-day trial
Read 559 reviewsTarget Test Prep

Compare the format, schedule, and included access before enrolling. Prices and seat counts shown reflect the supplied offer details.

Geometry: Decagon

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Junior | Next Rank: 30 Posts
Posts: 15
Joined: Tue Jul 09, 2013 12:53 pm
Thanked: 1 times
by Yaj » Sat Sep 14, 2013 6:02 am
Some help!!

The figure shows a regular decagon (10-side polygon). Angle x is formed by extending two of the sides of the decagon. What is the degree measure of angle x?
(A) 96
(B) 108
(C) 120
(D) 144
(E) 150

[spoiler]OA:B[/spoiler]

Thank You!
Attachments
Screen Shot 2013-09-14 at 7.30.36 PM.png
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Problem Solving |
User avatar
Legendary Member
Posts: 643
Joined: Wed Aug 14, 2013 4:27 amFollowed by: 7 members
Thanked: 48 times

by vinay1983 » Sat Sep 14, 2013 6:28 am
The interior angles of the decagon is equal to (n-2)*180, where n is equal to no.of sides

So, (10-2)*180 = 8 * 180 = 1440 i.e 1440/10 = 144 degrees. So let us name the triangle such formed(as per the figure) A B C in clockwise direction.

As per above each angle is equal to 144 degrees, so we know that on a straight line the angle is equal to 180 degrees so, 144+x=180 i.e x = 36 degrees (interior angle CAB and likewise angle BCA).

We also know that sum of interior angles of a triangle is 180 degrees, hence in triangle ABC angle (x as per your diagram)ABC + angle BAC + angle BCA = 180 degrees

Of this we know the value of angle CAB and angle BCA values, hence angle ABC = 180 - 2*36 = 180-72=108 degrees

Option B is correct.


I hope I am right!
You can, for example never foretell what any one man will do, but you can say with precision what an average number will be up to!
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members
Location: Vancouver, BC
Thanked: 5254 times
GMAT Score:770

Geometry: Decagon

by Brent@GMATPrepNow » Sat Sep 14, 2013 6:31 am
Image
The figure shows a regular decagon (10-side polygon). Angle x is formed by extending two of the sides of the decagon. What is the degree measure of angle x?
(A) 96
(B) 108
(C) 120
(D) 144
(E) 150
Nice rule: The sum of the interior angles in an N-sided polygon is equal to 180(N - 2) degrees

So, in a 10-sided polygon, the sum of the interior angles = 180(10 - 2) = 1440 degrees

Since the polygon is a REGULAR polygon, all 10 sides have the same length, and all 10 angles are equal.
So, if the sum of all 10 angles = 1440 degrees, then each angle must = 1440/10 = 144

So, we get:
Image

At this point, we can use the fact that angles on a line add to 180 degrees to conclude that the two angles inside the triangle are 36 degrees each.
Image

So, 36 + 36 + x = 180
x = 108

Answer: B

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1