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

Redeem

Regular pentagon P has all five diagonals drawn. What is the angle between two of these diagonals where they meet at a

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Moderator
Posts: 7187
Joined: Thu Sep 07, 2017 4:43 pm
Followed by:23 members

Regular pentagon P has all five diagonals drawn. What is the angle between two of these diagonals where they meet at a

by BTGmoderatorDC » Wed Aug 26, 2020 6:26 pm

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

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°



OA B

Source: Magoosh
Top
Source: — Problem Solving |

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 8087
Joined: Sat Apr 25, 2015 10:56 am
Location: Los Angeles, CA
Thanked: 43 times
Followed by:29 members

Re: Regular pentagon P has all five diagonals drawn. What is the angle between two of these diagonals where they meet at

by Scott@TargetTestPrep » Sun Aug 30, 2020 7:23 am
BTGmoderatorDC wrote: ↑
Wed Aug 26, 2020 6:26 pm
 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°



OA B

Source: Magoosh
Solution:
Pentagon.png
The sum of the interior angle measures of a polygon with n sides is calculated by the formula: sum = 180 x (n - 2). Thus, for a pentagon, which has 5 sides, the sum of all the interior angles is 180 x (5 - 2) = 540. Thus, each angle of a regular pentagon is 540/5 = 108 degrees.

When a diagonal is drawn, it creates an isosceles triangle of 36, 36 and 108 degrees. When two diagonals are drawn from the same vertex, they divide the angle of the pentagon into 3 angles, two of which are 36 degrees. If we let x = the measure of the angle between two diagonals, then we have:

36 + x + 36 = 108

x + 72 = 108

x = 36

Answer: B

Scott Woodbury-Stewart
Founder and CEO
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

ImageImage
Top
Post new topic Post Reply
• Page 1 of 1