1. What is the minimum interior angle possible for a regular polygon? Why? 2. What is the maximum exterior angle possible for a regular polygon?
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Answer:
For a regular polygon, as the number of sides increase, interior angle also increases and exterior angle decreases.
Therefore, polygon with minimum interior angle and maximum exterior angle is an equilateral triangle, as it has a minimum number of sides possible for a polygon i.e., 3.
(a) Interior angle of equilateral triangle is 60
0
, which is the minimum interior angle possible for the regular polygon.
(b) Exterior angle of an equilateral triangle is 180
0
−60
0
=120
0
, which is the maximum exterior angle possible for the regular polygon.
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- Triangle is the polygon with minimum number of sides and an equilateral triangle is a regular polygon because all sides are equal in this. We know that each angle of an equilateral triangle measures 60 degree. Hence, 60 degree is the minimum possible value for internal angle of a regular polygon.
- Obviously, n = 3, the exterior angle will be maximum. The sum of an interior angle and an exterior angle is always supplementary. So for an equilateral triangle, each exterior angle is 120° and interior angle is 60°. The maximum exterior angle possible for a regular polygon is 120°.
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