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# polygon

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what is the measure of one interior angle of a regular polygon?

Guest May 19, 2017
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fROM COOLMATH : All sides All sides are the same length (congruent) and all interior angles are the same size (congruent). To find the measure of the interior angles, we know that the sum of all the angles is 540 degrees (from above)... And there are five angles... So, the measure of the interior angle of a regular pentagon is 108 degrees.are the same length (congruent) and all interior angles are the same size (congruent). To find the measure of the interior angles, we know that the sum of all the angles is 540 degrees (from above)... And there are five angles... So, the measure of the interior angle of a regular pentagon is 108 degrees.

tertre  May 19, 2017
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To find the interior angle measure of one angle of any regular polygon, use this formula. Let n= the number of sides of the regular polygon

$$\frac{180(n-2)}{n}$$

Let's see this expression in action:

 Number of Sides Name of Regular Polygon Interior Angle Measure 3 Triangle $$\frac{180(3-2)}{3}=\frac{180*1}{3}=60$$ 4 Quadrilateral $$\frac{180(4-2)}{4}=\frac{180*2}{4}=90$$ 5 Pentagon $$\frac{180(5-2)}{5}=\frac{180*3}{5}=108$$ 6 Hexagon $$\frac{180(6-2)}{6}=\frac{180*4}{6}=120$$
Guest May 19, 2017