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Q: What shape has the smallest number of sides a regular polygon with obtuse angles can have?

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Interior angles 178 so exterior angles 2. Number of sides of any regular polygon = 360/exterior angle You polygon has 180 sides. Bet you're glad you didn't have to sketch it!

Yes and it is: sum of interior angles/number of sides

Exterior angles of ANY polygon add to 360 degrees. Individual angles are therefore 360/n where n is the number if sides. 72

If interior angles are 177o then exterior angles are 3o. Exterior angle times number of sides is always 360 so the polygon has 120 sides.

Assuming that the polygon is formed from a closed circuit of ray, then the number of ray and the number of angles will be equal.

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No. To elaborate, the smallest regular polygon, an equilateral triangle, has 60 degree interior angles. The next larger one, a square, has 90 degree interior angles. In fact, for any regular polygon, the interior angles measure 180*(n-2)/n degrees, where n is the number of sides. No polygon has less than 3 sides. Thus, no regular polygon can have interior angles less than 60 degrees.

i don't really get the "same number of sides" ----- the angles of a polygon are the same with other angles within the polygon, if it is a regular polygon, and there a formula for getting the total sum of angles which is 180X(N-2) where N is the number of sides.

(number of sides-2)*180 = total sum of interior angles

equation for any regular polygon when n = number of sides: 180(n-2)/n

A 6 sided polygon is called a Hexagon. The sum of the interior angles or a regular hexagon is 720 degrees.

No; apart from the fact that "regular number" of sides does not mean anything. What numbers do you consider to be regular and why? In any case, a regular polygon is one which has all sides of equal length AND all angles of equal measure. A square is the only regular 4-sided polygon. A rectangle has equal angles but not sides, a rhombus has equal sides but not angles. All other quadrilaterals fail on both counts.

When the sides of a regular polygon increases its interior angles also increases

Let n = the number of sides of a regular polygon The sum of the interior angles of a regular polygon (A) is found in this equation: A = 180º x (n-2) Obviously, n must be greater than or equal to 3

Interior angles 178 so exterior angles 2. Number of sides of any regular polygon = 360/exterior angle You polygon has 180 sides. Bet you're glad you didn't have to sketch it!

-- The exterior angles of a polygon add up to 360 degrees, no matter how many of them there are.-- The interior angles of a polygon add up to [ (180) times (number of sides minus 2) ].-- These are both true whether or not the polygon is 'regular'.

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