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If a represents the measure of an interior angle of a regular octagon

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Bunuel
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If a represents the measure of an interior angle of a regular octagon [#permalink] New post   30 Nov 2016, 03:03
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If a represents the measure of an interior angle of a regular octagon and b represents the measure of an interior angle of a regular pentagon, what is the ratio a:b?

A. 5:4
B. 4:3
C. 3:2
D. 7:4
E. 9:5
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prashantrchawla
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Re: If a represents the measure of an interior angle of a regular octagon [#permalink] New post   30 Nov 2016, 03:17
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To determine interior angle of a regular polygon having "n" number of sides is (n-2)/2*180.
For octagon, the value of individual angle = 135.
For pentagon, the value of individual angle = 108
135:108 = 5:4. Hence answer is A.
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Re: If a represents the measure of an interior angle of a regular octagon [#permalink] New post   30 Nov 2016, 03:46
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Bunuel wrote:
If a represents the measure of an interior angle of a regular octagon and b represents the measure of an interior angle of a regular pentagon, what is the ratio a:b?

A. 5:4
B. 4:3
C. 3:2
D. 7:4
E. 9:5


sum of interior angle is given by : (n-2) * 180

sum of interior angle of octagon: (8-2) * 180 = 1080. so for each angle 1080/8 = 135

sum of interior angle of pentagon: (5-2) * 180 = 540, so for eacg angle 540/5 = 108

135 : 108
5: 4

Ans: A
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Re: If a represents the measure of an interior angle of a regular octagon [#permalink] New post   01 Sep 2020, 09:10
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In an n-sided shape the angles sum to (n-2)(180). So in a regular n-sided shape, where each angle is the same, each angle must be (n-2)(180)/n. Plugging in 8 and 5, and finding the required ratio, we have:

[ (6)(180)/8 ] / (3)(180)/(5) ] = (6)(5)/(8)(3) = 5/4
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Re: If a represents the measure of an interior angle of a regular octagon [#permalink] New post   01 Sep 2020, 12:05
Bunuel wrote:
If a represents the measure of an interior angle of a regular octagon and b represents the measure of an interior angle of a regular pentagon, what is the ratio a:b?

A. 5:4
B. 4:3
C. 3:2
D. 7:4
E. 9:5


\(a = \frac{6*180}{8} = 135\)

\(b = \frac{3*180}{5} = 108\)

Now, \(a : b = 135 : 108 => 5 : 4\), Thus, Answer must be (A)
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Re: If a represents the measure of an interior angle of a regular octagon [#permalink]
01 Sep 2020, 12:05
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