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Regular polygon X has r sides, and each vertex has an angle measure of [#permalink]
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IMO answer is C.

Maximum angle for Polygon X can be 179, when the number of sides is 360( cannot be 180- it is a straight single line). Therefore polygon Q has 90 sides and hence interior angle is 176.

Note- Interior angle of a polygon is [((n-2)/ n ) x 180 ]. To get the largest integral value keep increasing n value such that denominator is the factor of numerator. Maximum value possible is 360. IF WE INCREASE FURTHER THE ANGLE VALUE WILL BE of format 179._ _ _
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Re: Regular polygon X has r sides, and each vertex has an angle measure of [#permalink]
Hi Skywalker18, I don't understand why we need the polygon X has the maximum value of interior angle so that the polygon Q has the greatest value of its angle? Could you help explain for me plz?
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Re: Regular polygon X has r sides, and each vertex has an angle measure of [#permalink]
BrentGMATPrepNow
Bunuel
Regular polygon X has r sides, and each vertex has an angle measure of s, an integer. If regular polygon Q has r/4 sides, what is the greatest possible value of t, the angle measure of each vertex of Polygon Q?

A. 2
B. 160
C. 176
D. 178
E. 179

Sum of all angles in an n-sided polygon \(= (n-2)(180°)\)

If the n-sided polygon is REGULAR, each interior angle in the n-sided polygon \(= \frac{(n-2)(180°)}{n}\)

The question tells us that, in polygon X, each angle is an INTEGER.
Since each angle in a regular polygon must be LESS THAN 180°, 179° must be the biggest possible angle in polygon X

So we can write: \(\frac{(n-2)(180)}{n} = 179\) [we'll solve this equation for n]

Multiply both sides by n to get: \((n-2)(180) = 179n\)

Expand the left side to get: \(180n-360 = 179n\)

Solve: \(n = 360\)

So, when polygon X has 360 sides, each interior angle is 179° (the greatest integer value for an interior angle in a regular polygon)

Now that we've maximized the measurement of each angle in polygon X, we can focus our attention on polygon Q

We're told that the number of sides in polygon Q is 1/4 the number of sides in polygon X

So, the number of sides in polygon Q = 360/4 = 90

When we plug 90 into our formula above, we get...

Each angle in a 90-sided polygon \(= \frac{(90-2)(180)}{90}= \frac{(88)(2)}{1}=176\)

Answer: C

Cheers,
Brent

Hi Brent BrentGMATPrepNow, given If regular polygon Q has r/4 sides, how do we know r is 360 here? As question did not state that "If regular polygon Q has r/4 sides of polygon X ". Did I miss something here? Thanks Brent.
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Regular polygon X has r sides, and each vertex has an angle measure of [#permalink]
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Kimberly77
Hi Brent BrentGMATPrepNow, given If regular polygon Q has r/4 sides, how do we know r is 360 here? As question did not state that "If regular polygon Q has r/4 sides of polygon X ". Did I miss something here? Thanks Brent.

Given: Regular polygon Q has r/4 sides
Given: Regular polygon X has r sides and each vertex has an angle measure of s,
Question: What is the greatest possible value of t, the angle measure of each vertex of Polygon Q?

Notice that both polygons are related by the value of r

So, in order to maximize the value of t, we need to maximize the number of sides and polygon Q.
This also means we need to maximize the number of sides in polygons X (which is what we did to conclude that \(n = 360\)
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Re: Regular polygon X has r sides, and each vertex has an angle measure of [#permalink]
BrentGMATPrepNow
Kimberly77
Hi Brent BrentGMATPrepNow, given If regular polygon Q has r/4 sides, how do we know r is 360 here? As question did not state that "If regular polygon Q has r/4 sides of polygon X ". Did I miss something here? Thanks Brent.

Given: Regular polygon Q has r/4 sides
Given: Regular polygon X has r sides and each vertex has an angle measure of s,
Question: What is the greatest possible value of t, the angle measure of each vertex of Polygon Q?

Notice that both polygons are related by the value of r

So, in order to maximize the value of t, we need to maximize the number of sides and polygon Q.
This also means we need to maximize the number of sides in polygons X (which is what we did to conclude that \(n = 360\)

Gerat explanation BrentGMATPrepNow. I knew I was missing something...devil is in the details :facepalm_man: :lol: thanks Brent :please:
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Re: Regular polygon X has r sides, and each vertex has an angle measure of [#permalink]
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