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# Each interior angle of a regular polygon is 120 degrees greater than

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Joined: 02 Sep 2009
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Each interior angle of a regular polygon is 120 degrees greater than  [#permalink]

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29 Jan 2019, 09:09
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Difficulty:

65% (hard)

Question Stats:

48% (02:28) correct 52% (01:42) wrong based on 35 sessions

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Each interior angle of a regular polygon is 120 degrees greater than each exterior angle. How many sides are there in the polygon?

A. 6 sides
B. 8 sides
C. 10 sides
D. 12 sides
E. 13 sides

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Re: Each interior angle of a regular polygon is 120 degrees greater than  [#permalink]

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29 Jan 2019, 09:46
1
Bunuel wrote:
Each interior angle of a regular polygon is 120 degrees greater than each exterior angle. How many sides are there in the polygon?

A. 6 sides
B. 8 sides
C. 10 sides
D. 12 sides
E. 13 sides

each exterior angle = 360/n
each interior angle = 180-360/n
so
at n =12
exterior angle = 360/12 = 30
interior angle = 180-30 = 150

difference interior and exterior angle = 150-30 = 120
IMO D
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Re: Each interior angle of a regular polygon is 120 degrees greater than  [#permalink]

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29 Jan 2019, 09:57
1
I+E = 180
I-E =120
I = 150
150= [(n-2)180]/n
n=12 = no of sides = answer
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Re: Each interior angle of a regular polygon is 120 degrees greater than  [#permalink]

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01 Feb 2019, 09:15
Bunuel wrote:
Each interior angle of a regular polygon is 120 degrees greater than each exterior angle. How many sides are there in the polygon?

A. 6 sides
B. 8 sides
C. 10 sides
D. 12 sides
E. 13 sides

Since the sum of the interior and exterior angle of a polygon is 180, we can let the exterior angle = x and the interior angle = 120 + x. We can create the equation:

x + 120 + x = 180

2x = 60

x = 30

Since the sum of the measures of all the exterior angles of a polygon = 360, the polygon has 360/30 = 12 sides.

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Re: Each interior angle of a regular polygon is 120 degrees greater than   [#permalink] 01 Feb 2019, 09:15
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