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Which of the following cannot be interior angle of a regular polygon?
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02 Apr 2021, 08:33
02 Apr 2021, 08:33
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Which of the following cannot be an interior angle of a regular polygon (in degrees)?
A. 162
B. 150
C. 144
D. 140
E. 125
A. 162
B. 150
C. 144
D. 140
E. 125
Which of the following cannot be interior angle of a regular polygon?
[#permalink]
02 Apr 2021, 18:55
02 Apr 2021, 18:55
1
To find the sum of all interior angles of a polygon with n sides, we use the equation, sum of interior angles = (n-2) * 180. To find each angle of regular polygon, we divide this sum by n. Let's use this in this question.
If x is measure of interior angle,
[(n-2) * 180] / n = x
[180n - 360] / n = x
180 - (360/n) = x
180 - x = 360 / n
n = 360 / (180 - x)
Now plugin each answer choice for x. If n turns out to be an integer, eliminate because number of sides n must be an integer.
Only for x = 125 you will find n ≠ integer.
Hence, E is the correct answer.
Posted from my mobile device
If x is measure of interior angle,
[(n-2) * 180] / n = x
[180n - 360] / n = x
180 - (360/n) = x
180 - x = 360 / n
n = 360 / (180 - x)
Now plugin each answer choice for x. If n turns out to be an integer, eliminate because number of sides n must be an integer.
Only for x = 125 you will find n ≠ integer.
Hence, E is the correct answer.
Posted from my mobile device
gmatclubot
Which of the following cannot be interior angle of a regular polygon? [#permalink]
02 Apr 2021, 18:55
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