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Arup Dutta

· started a discussion

· 1 Months ago

provide correct explanation (Question: 78050.0 )

please correct the explanation as there is two unkbown in the equation

Question:
The difference between the exterior and interior angles at a vertex of a regular polygon is 1500. The number of sides of the polygon is:
Options:
A) 10
B) 15
C) 24
D) 30
Solution:

Let the no. of sides of polygon be n.

Then,

\(\big(\cfrac{2n-4}{n}\big)×90^o-\cfrac{360}{n}=150\)

6n – 24 = 5n

n = 24

Knowledge Expert

· commented

· 1 Months ago

Let interior angle be X and exterior angle be Y So, we can write them as X-Y=150 degrees and X+Y=180 degrees in order to find the number of sides of a polygon the formula is 360 degrees/interior angle so by solving above two equations we get X= 15 degrees so 360 degrees/15 degrees n=24 sides
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