If the sum of all interior angles of a regular polygon is twice the sum of all its exterior angles then the polygon is
Hexagon
This question involves understanding the properties of regular polygons, specifically the relationship between their interior and exterior angles. A regular polygon is a polygon that is equiangular (all angles are equal in measure) and equilateral (all sides have the same length).
To solve this problem, we need two key formulas:
The question states a specific condition: "the sum of all interior angles of a regular polygon is twice the sum of all its exterior angles". We can translate this statement into a mathematical equation using the formulas above.
Given condition: \(S_i = 2 \times S_e\)
Substituting the formulas:
\[ (n-2) \times 180^\circ = 2 \times 360^\circ \]Now, we need to solve this equation to find the value of '\(n\)', which tells us the number of sides the polygon has.
The calculation shows that the polygon has 6 sides.
A polygon with 6 sides is known as a Hexagon. Therefore, the regular polygon described in the question is a Hexagon.
Comparing this result with the given options:
Our calculated value of \(n=6\) corresponds to a Hexagon.
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