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10 Feb 2021, 06:45
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
60% (01:38) correct
40%
(02:06)
wrong
based on 47
sessions
History
Date
Time
Result
Not Attempted Yet
The interior angles of a regular polygon measure 150º each. The number of diagonals of the polygon is
(A) 35
(B) 44
(C) 54
(D) 78
(E) 88
Are You Up For the Challenge: 700 Level Questions: 700 Level Questions
(A) 35
(B) 44
(C) 54
(D) 78
(E) 88
Are You Up For the Challenge: 700 Level Questions: 700 Level Questions
10 Feb 2021, 07:24
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Bunuel
FOr interior angle = 150o
Exterior angle = 180-150 = 30o
Exterior Angle in a Regular Polygon\( = \frac{360o}{n}\) where n = Number of sides of polygon
i.e. \(30o= \frac{360o}{n}\)
i.e. \(n = 12\)
Number of diagonals in a 12 sides polygon = \(^{12}C_2 - 12 = 66-12 = 54\)
Answer: Option C
General Discussion
wishmasterdj
Joined: 04 May 2016
Last visit: 25 Oct 2021
Posts: 91
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Given Kudos: 10
Location: India
Schools: ISB '18 (A)
GMAT 1: 700 Q48 V37
GPA: 3.2
14 Feb 2021, 04:13
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150*n can be equated with sum of interior angles formula:
150*n = 180 (n-2)
Solving it we get n=12
This polygon has both 12 sides, and thus vertices. Now for diagonals, take any point, you can make a diagonal with n-3 points
(three excluded ones are itself and the two adjacent ones on either side).
Thus, 12*9 /2 (divide by 2 to avoid double counting diagonals AD and DA, since you are oging along the vertices adding up the diagonals)
Thus 54 (C) is the answer
150*n = 180 (n-2)
Solving it we get n=12
This polygon has both 12 sides, and thus vertices. Now for diagonals, take any point, you can make a diagonal with n-3 points
(three excluded ones are itself and the two adjacent ones on either side).
Thus, 12*9 /2 (divide by 2 to avoid double counting diagonals AD and DA, since you are oging along the vertices adding up the diagonals)
Thus 54 (C) is the answer
