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The logo of a certain corporation is in the shape

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by NandishSS » Thu May 04, 2017 6:44 am
The logo of a certain corporation is in the shape of a polygon, where all angles of a the polygon have equal measures. In the above figure V is one vertex of the polygon. If Y in degrees is the measure of an angle of the polygon and y=5x how many sides does the polygon have?

A 5
B 6
C 10
D 12
E 30

OA:D

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by GMATGuruNY » Thu May 04, 2017 7:03 am
NandishSS wrote:The logo of a certain corporation is in the shape of a polygon, where all angles of a the polygon have equal measures. In the above figure V is one vertex of the polygon. If Y in degrees is the measure of an angle of the polygon and y=5x how many sides does the polygon have?

A 5
B 6
C 10
D 12
E 30
Since y and x form a straight line, y+x = 180.
Substituting y=5x into y+x=180, we get:
5x+x = 180
6x = 180
x = 30, implying that y = 5*30 = 150.

The sum of the angles inside a polygon = (n-2)(180), where n is the number of sides and the number of angles.
If all the angles are equal, then the measure of each angle = (sum of the angles)/(number of angles) = [(n-2)(180)]/n.
Since the measure of each angle in the logo = 150, we get:
[(n-2)(180)]/n = 150
180n - 360 = 150n
30n = 360
n = 12.

The correct answer is D.
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by [email protected] » Thu May 04, 2017 8:21 am
Hi NandishSS,

One of the rarer rules that can appear on the GMAT is "add a side, add 180 degrees"

For example
A triangle = 180 degrees
A 4-sided shape = 360 degrees
A 5-sided shape = 540 degrees
A 6-sided shape = 720 degrees
Etc.

In this prompt, we can use a combination of Geometry rules and the Answer choices to TEST THE ANSWERS.

To start, we have to figure out the values of X and Y. Since those two angles form a line (thus, X+Y = 180) and Y = 5X, then X+5X = 180.... X=30 and Y=150

We're told that each of the angles in this unknown polygon is the SAME. We're asked for the number of sides that this polygon has.

Using the above math rule, and the answer choices, we can work our way through the list until we find the polygon with equal 150 degree angles. Let's start with Answer B...

Answer B: 6-sided

A 6-sided shape = 720 degrees
720/(6 sides) = 120 degrees per side
This is TOO SMALL (it's supposed to be 150 degrees), so we clearly need more sides/more degrees.

Answer D: 12-sided

A 12-sided shape = 180 + 9(180) = (10)180 = 1800 degrees
1800/(12 sides) = 150 degrees per side
This is an exact MATCH for what we were told, so this must be the answer.

Final Answer: D

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