Question : If the external angle of a regular polygon is 18°, then the number of diagonals in this polygon is:
Option 1: 180
Option 2: 150
Option 3: 170
Option 4: 140
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Correct Answer: 170
Solution :
Given,
Each exterior angle of a polygon is 18°.
We know that the sum of the exterior angles of a polygon is 360°.
Number of sides of polygon = $\frac{360°}{\text{each exterior angle}}$
⇒ Number of sides of regular polygon, $n$ = $\frac{360°}{18°} = 20$
$\therefore$ Number of diagonals = $\frac{n(n-3)}{2}=\frac{20(20-3)}{2}=170$
Hence, the correct answer is 170.
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