Which of the following can't represent the degree measure of an equian

Question

Which of the following can't represent the degree measure of an equiangular polygon ?

(A) 160
(B) 150
(C) 140
(D) 130
(E) 120

ScottTargetTestPrep · Accepted Answer

Solution:

Recall that the sum of the measures of all the angles of an n-sided polygon is 180(n - 2) degrees. Therefore, if the polygon is equiangular, the measure of each angle is m = 180(n - 2)/n degrees. Now let’s check each answer choice.

A) 160

If m = 160, we have:

160 = 180(n - 2)/n

160n = 180n - 360

360 = 20n

18 = n

So m can be 160.

B) 150

If m = 150, we have:

150 = 180(n - 2)/n

150n = 180n - 360

360 = 30n

12 = n

So m can be 150.

C) 140

If m = 140, we have:

140 = 180(n - 2)/n

140n = 180n - 360

360 = 40n

9 = n

So m can be 140.

D) 130

If m = 130, we have:

130 = 180(n - 2)/n

130n = 180n - 360

360 = 50n

7.2 = n

Since n must be an integer, we see that m CAN’T be 130.

Alternate Solution:

Recall that the sum of the measures of all the angles of an n-sided polygon is 180(n - 2) degrees. Therefore, if the polygon is equiangular, the measure of each angle is m = 180(n - 2)/n degrees. Let’s solve this equation for n:

nm = 180n - 360

360 = 180n - nm

360 = n(180 - m)

n = 360/(180 - m)

Since the number of sides in a polygon is an integer, n = 360/(180 - m) must be an integer. Checking each answer choice, we notice that all the choices except m = 130 result in an integer value for n.

Answer: D

Archit3110 · Answer

each interior angle = 180-360/n
use plugin and solve , we dont get integer value at 130
IMO D

sujoykrdatta · Answer

Solution:

The options represent the interior angles. Let's canculate the exterior angles:

A) 20
B) 30
C) 40
D) 50
E) 60

Each exterior angle is simply 360/n where n is the number of sides (an integer). Thus, we can say: 
n (no. of sides) = 360/(each ext. angle)

Thus, each ext. angle must be a factor of 360.

Only Option D has a number, 50, that is not a factor of 360.

Answer D

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IanStewart · Answer

There are a couple of other ways to quickly see that 130 is impossible. If you know that a regular hexagon has 120 degree angles, and a regular octagon has 135 degree angles, then if you can see that a regular 7-sided shape will have non-integer angles (since we can't divide (n-2)*180 by 7 evenly), 130 must be impossible, since as n gets bigger, the size of the angles gets bigger. Or you might be able to see that the equation (n-2)*180/n = 130 can't have an integer solution for n, because 13 is a factor of the right side, and could only be a factor of the left side if n is 15 or greater, but the angles in a regular 15-sided shape will be much larger than 130 degrees.

naveeng15 · Answer

sum of all interior angles in a polygon in (n-2)180degree

so for equiangular (n-2)180/n = angle

so substitute each option

we get as option D

gmatpro15 · Answer

each interior angle = 180-360/n
use plugin and solve , we dont get integer value at 130
IMO D

Which of the following can't represent the degree measure of an equian

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Which of the following can't represent the degree measure of an equian

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