The native polygon is a mix of 2 Greek words: "poly" way many and "gon" way angle. In addition to its angles, a polygon likewise has sides and also vertices. "Tri" way "three," therefore the most basic polygon is called the triangle, since it has actually three angles. It additionally has 3 sides and three vertices. A triangle is constantly coplanar, i m sorry is not true of numerous of the other polygons.

A constant polygon is a polygon v all angles and all sides congruent, or equal. Right here are some regular polygons.


We deserve to use a formula to uncover the amount of the interior angles of any kind of polygon. In this formula, the letter n stands for the number of sides, or angles, that the polygon has.

sum of angles = (n – 2)180°

Let"s usage the formula to uncover the sum of the interior angles of a triangle. Instead of 3 because that n. We find that the sum is 180 degrees. This is an essential fact come remember.

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sum of angles = (n – 2)180° = (3 – 2)180° = (1)180° = 180°

To find the sum of the internal angles the a quadrilateral, we can use the formula again. This time, instead of 4 for n. We find that the amount of the interior angles of a quadrilateral is 360 degrees.

sum of angles = (n – 2)180° = (4 – 2)180° = (2)180° = 360°

Polygons deserve to be separated right into triangles by illustration all the diagonals that can be drawn from one single vertex. Let"s try it through the quadrilateral presented here. Indigenous vertex A, us can draw only one diagonal, to vertex D. A quadrilateral can because of this be separated right into two triangles.


If girlfriend look earlier at the formula, you"ll see that n – 2 gives the variety of triangles in the polygon, and that number is multiplied by 180, the sum of the measures of every the inner angles in a triangle. Do you check out where the "n – 2" come from? It gives us the number of triangles in the polygon. How many triangles do you think a 5-sided polygon will have?


Here"s a pentagon, a 5-sided polygon. From vertex A us can attract two diagonals i m sorry separates the pentagon right into three triangles. Us multiply 3 times 180 levels to find the amount of all the inner angles of a pentagon, i beg your pardon is 540 degrees.

sum of angles = (n – 2)180° = (5 – 2)180° = (3)180° = 540°

Related Links: Polygon definitions, p olygon formulas (area, perimeter) and polygon surname (Tables and also Formulas)

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Homework help | Geometry | Polygons
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