Events & Promotions
|
|
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Nov 1912:30 PM EST
-01:30 PM EST
Learn how Keshav, a Chartered Accountant, scored an impressive 705 on GMAT in just 30 days with GMATWhiz's expert guidance. In this video, he shares preparation tips and strategies that worked for him, including the mock, time management, and more
Nov 2001:30 PM EST
-02:30 PM IST
Learn how Kamakshi achieved a GMAT 675 with an impressive 96th %ile in Data Insights. Discover the unique methods and exam strategies that helped her excel in DI along with other sections for a balanced and high score.
Nov 2211:00 AM IST
-01:00 PM IST
Do RC/MSR passages scare you? e-GMAT is conducting a masterclass to help you learn – Learn effective reading strategies Tackle difficult RC & MSR with confidence Excel in timed test environment- Nov 23
11:00 AM IST
-01:00 PM IST
Attend this free GMAT Algebra Webinar and learn how to master the most challenging Inequalities and Absolute Value problems with ease. 
Nov 2407:00 PM PST
-08:00 PM PST
Full-length FE mock with insightful analytics, weakness diagnosis, and video explanations!
Nov 2510:00 AM EST
-11:00 AM EST
Prefer video-based learning? The Target Test Prep OnDemand course is a one-of-a-kind video masterclass featuring 400 hours of lecture-style teaching by Scott Woodbury-Stewart, founder of Target Test Prep and one of the most accomplished GMAT instructors.
AbdurRakib
Joined: 11 May 2014
Last visit: 08 Nov 2025
Posts: 465
Given Kudos: 220
Status:I don't stop when I'm Tired,I stop when I'm done
Location: Bangladesh
Concentration: Finance, Leadership
Schools: Wharton '20 Yale '20 Tepper '20
GPA: 2.81
WE:Business Development (Real Estate)
Updated on: 01 Oct 2018, 10:26
Originally posted by AbdurRakib on 16 Jun 2017, 08:01.
Last edited by bb on 01 Oct 2018, 10:26, edited 2 times in total.
Last edited by bb on 01 Oct 2018, 10:26, edited 2 times in total.
Edited the question.
Kudos
Bookmarks
A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
70% (02:29) correct
30%
(02:29)
wrong
based on 4725
sessions
History
Date
Time
Result
Not Attempted Yet
The figure shown above consists of a shaded 9-sided polygon and 9 unshaded isosceles triangles.For each isosceles triangle,the longest side is a side of the shaded polygon and the two sides of equal length are extensions of the two adjacent sides of the shaded polygon.What is the value of a ?
A. 100
B. 105
C. 110
D. 115
E. 120
OG 2019 PS00947
Attachment:
11qk4nq.jpg [ 4.72 KiB | Viewed 103300 times ]
Updated on: 10 Feb 2021, 07:48
Originally posted by BrentGMATPrepNow on 27 Jun 2017, 15:06.
Last edited by BrentGMATPrepNow on 10 Feb 2021, 07:48, edited 3 times in total.
Last edited by BrentGMATPrepNow on 10 Feb 2021, 07:48, edited 3 times in total.
Kudos
Bookmarks
AbdurRakib
Although the 9-sided polygon is NOT a regular polygon (with equal angles and equal sides), we CAN show that the angles are all equal.
The key here is that each of the unshaded triangles is an isosceles triangle.
So, for example, we know that the two angles with the red dots are equal.
Since the next angle over is opposite the angle with the red dot, we know that that angle is also equal to the other two angles (see the diagram below)
Since the next triangle is ISOSCELES, we know that its other angle is equal to the first (see the diagram below)
We can continue applying the same rules and logic to see that all of the red dotted angles are all equal.
Next, if all of the red-dotted angles are equal, then all of the angles denoted with x are all equal, since each of those angles is on a line with the red-dotted angle.
To determine the value of x, we'll use the following rule:
the sum of the angles in an n-sided polygon = (n - 2)(180º)
So, in a 9-sided polygon, the sum of ALL 9 angles = (9 - 2)(180º) = (7)(180º)
So, EACH individual angle = (7)(180º)/9 = 140º
Also, since the red-dotted angle is on the line with the 140º, the red-dotted angle = 40º
Let's add this information to the diagram below:
Since the unshaded triangle is isosceles, the other angle is also 40º
Since all three angles in the triangle must add to 180º, the last remaining angle (aº) must be 100º
Answer:
RELATED VIDEOS
16 Jun 2017, 08:24
Kudos
Bookmarks
In an n-sided polygon the sum of internal angles is (n-2)*180 degree
So, the 9-sided polygon has sum of internal angles as 7*180 degree,
making each of the individual angles \(\frac{7*180}{9}\) = 140 degree
Lets name the other two angles of the triangle with angle a as b and c.
Since we know that the triangles(isosceles) has two sides of equal length as extensions,
we know that
1. b=c (angles opposite equal sides are equal in magnitude)
2. a+b+c =180 degree (sum of angles in a triangle is 180 degree)
Since the sum of the angles in a straight line is 180 degree, b+140 = 180.
Thus b = c = 40 degree
Using this information in a+b+c =180 degree, we can deduce that a = 100(Option A)
So, the 9-sided polygon has sum of internal angles as 7*180 degree,
making each of the individual angles \(\frac{7*180}{9}\) = 140 degree
Lets name the other two angles of the triangle with angle a as b and c.
Since we know that the triangles(isosceles) has two sides of equal length as extensions,
we know that
1. b=c (angles opposite equal sides are equal in magnitude)
2. a+b+c =180 degree (sum of angles in a triangle is 180 degree)
Since the sum of the angles in a straight line is 180 degree, b+140 = 180.
Thus b = c = 40 degree
Using this information in a+b+c =180 degree, we can deduce that a = 100(Option A)
