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Math Expert V
Joined: 02 Sep 2009
Posts: 62499
A polygon has two types of angles: it has m 125º angles and n 150º ang  [#permalink]

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Difficulty:   75% (hard)

Question Stats: 63% (02:15) correct 38% (01:56) wrong based on 24 sessions

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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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Director  P
Joined: 25 Jul 2018
Posts: 628
Re: A polygon has two types of angles: it has m 125º angles and n 150º ang  [#permalink]

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1
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

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Director  D
Joined: 07 Mar 2019
Posts: 911
Location: India
GMAT 1: 580 Q43 V27
WE: Sales (Energy and Utilities)
Re: A polygon has two types of angles: it has m 125º angles and n 150º ang  [#permalink]

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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

Posted from my mobile device

Since in a polygon
number of angles = number of sides
x = m + n
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Ephemeral Epiphany..!

GMATPREP1 590(Q48,V23) March 6, 2019
GMATPREP2 610(Q44,V29) June 10, 2019
GMATPREPSoft1 680(Q48,V35) June 26, 2019 Re: A polygon has two types of angles: it has m 125º angles and n 150º ang   [#permalink] 20 Feb 2020, 05:37
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# A polygon has two types of angles: it has m 125º angles and n 150º ang  