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What is the degree measure of an internal angle of a polygon with 12 s

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Bunuel
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What is the degree measure of an internal angle of a polygon with 12 s [#permalink] New post   17 Feb 2020, 08:33
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What is the degree measure of an internal angle of a polygon with 12 sides, all equal in length?

A. 30 degrees
B. 60 degrees
C. 120 degrees
D. 135 degrees
E. 150 degrees
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E
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Re: What is the degree measure of an internal angle of a polygon with 12 s [#permalink] New post   18 Feb 2020, 02:47
Bunuel wrote:
What is the degree measure of an internal angle of a polygon with 12 sides, all equal in length?

A. 30 degrees
B. 60 degrees
C. 120 degrees
D. 135 degrees
E. 150 degrees


interior angle ; 180-360/no of sides
180-360/12 ; 150
IMO E
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Re: What is the degree measure of an internal angle of a polygon with 12 s [#permalink] New post   18 Feb 2020, 12:27
(12-2)*180/12=150

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Re: What is the degree measure of an internal angle of a polygon with 12 s [#permalink] New post   22 Feb 2020, 03:36
We know that internal angle of any polygon is given by ({N-2} X 180)/ N
where N is the number of sides of the polygon.

Hence for N=12, internal angle of the polygon is (12-2)x180/12=150.

Or, answer is Option E.
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Re: What is the degree measure of an internal angle of a polygon with 12 s [#permalink] New post   22 Feb 2020, 23:18
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Solution



Given
In this question, we are given that
    • A polygon with 12 sides, all equal in length

To find
We need to determine
    • The degree measure of an internal angle of that polygon

Approach and Working out
For a regular polygon with n number of sides, sum of all the internal angles = (2n – 4) x 90
Here, n = 12
    • Hence, sum of all angles = (2 x 12 – 4) x 90 = 1800
    • Therefore, measure of each angle = 1800/12 = 150

Thus, option E is the correct answer.

Correct Answer: Option E
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Re: What is the degree measure of an internal angle of a polygon with 12 s [#permalink]
22 Feb 2020, 23:18
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