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

Redeem

The figure shows that l is parallel to m. What is ∠ x+∠

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Elite Legendary Member
Posts: 3991
Joined: Fri Jul 24, 2015 2:28 am
Location: Las Vegas, USA
Thanked: 19 times
Followed by:37 members

The figure shows that l is parallel to m. What is ∠ x+∠

by Max@Math Revolution » Wed Oct 16, 2019 1:16 am
[GMAT math practice question]

The figure shows that l is parallel to m. What is ∠ x+∠ y+∠ z+∠ p+∠ q+∠ r?

A. 90
B. 100
C. 160
D. 180
E. 190


Image
Top
Source: — Problem Solving |
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

by GMATGuruNY » Thu Oct 17, 2019 2:45 am
For any polygon with n sides, the sum of the interior angles = (n-2)(180).
In a DECAGON -- a polygon with 10 sides -- the sum of the interior angles = (10-2)(180) = 1440.
If a regular decagon -- a decagon with 10 equal sides and 10 equal angles -- the degree measurement of each angle = 1440/10 = 144.

To solve the problem above, we can redraw the figure so that x, y, z, p, q and r are exterior angles for a regular decagon, as shown in the figure below:
Image
In the redrawn figure, x+y+z+p+q+r = 18+36+36+36+36+18 = 180.

The correct answer is D.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Top
User avatar
Elite Legendary Member
Posts: 3991
Joined: Fri Jul 24, 2015 2:28 am
Location: Las Vegas, USA
Thanked: 19 times
Followed by:37 members

by Max@Math Revolution » Fri Oct 18, 2019 1:40 am
=>

When we draw parallel lines passing through the point Q, we have the following figure.
Then we have < x+< y+< z+< p+< q+< r = 180°.

Image

Therefore, D is the answer.
Answer: D
Top
Post new topic Post Reply
• Page 1 of 1