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A polygon has two types of angles: it has m 125º angles and n 150º ang

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Bunuel
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A polygon has two types of angles: it has m 125º angles and n 150º ang [#permalink] New post   20 Feb 2020, 05:27
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A polygon has two types of angles: it has m 125º angles and n 150º angles, where m and n are positive integers. What is the value of |m − n| ?

A. 1

B. 3

C. 5

D. 6

E. 12


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C
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lacktutor
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Re: A polygon has two types of angles: it has m 125º angles and n 150º ang [#permalink] New post   20 Feb 2020, 05:44
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The sum of interior angles:
—> 180(x—2)
(—> x= the number of angles)

x= m+n
—> 125m + 150n = 180(m+n—2)
125m + 150n = 180m+180n—360
55m + 30n = 360
—> 11m+ 6n = 72
m,n — positive integer
Only m=6 and n = 1 satisfies the equation ( 11*6 + 6*1= 72)
| m—n | = 6–1= 5

The answer is C

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Re: A polygon has two types of angles: it has m 125º angles and n 150º ang [#permalink] New post   20 Feb 2020, 06:37
lacktutor wrote:
The sum of interior angles:
—> 180(x—2)
(—> x= the number of angles)

x= m+n
—> 125m + 150n = 180(m+n—2)
125m + 150n = 180m+180n—360
55m + 30n = 360
—> 11m+ 6n = 72
m,n — positive integer
Only m=6 and n = 1 satisfies the equation ( 11*6 + 6*1= 72)
| m—n | = 6–1= 5

The answer is C

Posted from my mobile device

Since in a polygon
number of angles = number of sides
x = m + n
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Re: A polygon has two types of angles: it has m 125º angles and n 150º ang [#permalink] New post   11 Nov 2023, 22:41
Bunuel wrote:
A polygon has two types of angles: it has m 125º angles and n 150º angles, where m and n are positive integers. What is the value of |m − n| ?

A. 1

B. 3

C. 5

D. 6

E. 12


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The external angles of a polygon always add upto 360 degrees. Hence we have

m(180 - 125) + n(180 - 150) = 360
=> 55m + 30n = 360
=> 11m + 6n = 72

We can see that m = 6 and n = 1 fulfils the equations, hence
| m - n | = | 6 - 1 | = 5

Option C
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Re: A polygon has two types of angles: it has m 125º angles and n 150º ang [#permalink]
11 Nov 2023, 22:41
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