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.
Apr 2601:30 AM EDT
-02:30 AM EDT
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.
Apr 2610:00 AM EDT
-11:00 AM EDT
The Target Test Prep course represents a quantum leap forward in GMAT preparation, a radical reinterpretation of the way that students should study. Try before you buy with a 5-day, full-access trial of the course for FREE!
Apr 2512:30 AM EDT
-01:30 AM EDT
At one point, she believed GMAT wasn’t for her. After scoring 595, self-doubt crept in and she questioned her potential. But instead of quitting, she made the right strategic changes. The result? A remarkable comeback to 695. Check out how Saakshi did it.
Apr 2711:00 AM EDT
-12:00 PM EDT
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
Apr 2808:00 AM PDT
-11:00 AM PDT
Whether you are just beginning your MBA journey or fine-tuning your path to a 700+ score, GMAT Day is designed to give you a competitive edge.
May 0111:00 AM PDT
-12:00 PM PDT
Free- full-length test + 15 concept videos + 150+ short videos + study plan!
06 Sep 2016, 17:12
Kudos
Bookmarks
B
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:
61% (01:59) correct
39%
(01:41)
wrong
based on 145
sessions
History
Date
Time
Result
Not Attempted Yet
Regular pentagon P has all five diagonals drawn. What is the angle between two of these diagonals where they meet at a vertex of the pentagon?
(A) 12°
(B) 36°
(C) 54°
(D) 60°
(E) 72°
(A) 12°
(B) 36°
(C) 54°
(D) 60°
(E) 72°
06 Sep 2016, 18:33
Kudos
Bookmarks
Few important points that we need to solve this question:
Exterior angle of a regular polygon = 360°/ n, n = number of sides of the regular polygon
Interior angle = 180° - exterior angle
Regular polygon has all sides equal
Regular polygon has same measure for each of the exterior and interior angles
Here, we have a regular pentagon. So, n = 5.
Exterior angle of a regular pentagon = 360°/ 5 = 72°
Interior angle of a regular pentagon = 180° - 72° = 108°
We are asked to find the angle between two diagonals where they meet at a vertex. If you draw a pentagon and connect all the diagonals, you will notice that we are asked to find the measure of a "portion" of the interior angle.
Next, note that the triangle formed with two sides of the pentagon and a diagonal is an isosceles triangle and the largest angle will be the interior angle. This means that measure of two smaller equal angles = (180° - 108°) / 2 = 36°.
Same will apply to all such isosceles triangles (two sides of the pentagon and a diagonal) formed within the regular pentagon.
For this question, we need two such isosceles triangles. Each will contribute one smaller angle, 36°.
Angle between diagonals = 108° - 36° - 36° = 36°
Answer (B).
Due to lack of visuals, the explanation may look complicated. If you draw and follow the story, it may make sense.
Exterior angle of a regular polygon = 360°/ n, n = number of sides of the regular polygon
Interior angle = 180° - exterior angle
Regular polygon has all sides equal
Regular polygon has same measure for each of the exterior and interior angles
Here, we have a regular pentagon. So, n = 5.
Exterior angle of a regular pentagon = 360°/ 5 = 72°
Interior angle of a regular pentagon = 180° - 72° = 108°
We are asked to find the angle between two diagonals where they meet at a vertex. If you draw a pentagon and connect all the diagonals, you will notice that we are asked to find the measure of a "portion" of the interior angle.
Next, note that the triangle formed with two sides of the pentagon and a diagonal is an isosceles triangle and the largest angle will be the interior angle. This means that measure of two smaller equal angles = (180° - 108°) / 2 = 36°.
Same will apply to all such isosceles triangles (two sides of the pentagon and a diagonal) formed within the regular pentagon.
For this question, we need two such isosceles triangles. Each will contribute one smaller angle, 36°.
Angle between diagonals = 108° - 36° - 36° = 36°
Answer (B).
Due to lack of visuals, the explanation may look complicated. If you draw and follow the story, it may make sense.
