Quick Answer: What Is The Formula For Finding The Interior Angles Of A Polygon?

What is the interior angle of a polygon?

The interior angles of a polygon are those angles at each vertex that are on the inside of the polygon.

There is one per vertex.

So for a polygon with N sides, there are N vertices and N interior angles.

Notice that for any given number of sides, all the interior angles are the same..

What is not a regular polygon?

An irregular polygon is any polygon that is not a regular polygon. … It can have sides of any length and each interior angle can be any measure. They can be convex or concave, but all concave polygons are irregular since the interior angles cannot all be the same.

What do alternate interior angles look like?

When two lines are crossed by another line (called the Transversal): Alternate Interior Angles are a pair of angles on the inner side of each of those two lines but on opposite sides of the transversal. In this example, these are two pairs of Alternate Interior Angles: c and f.

What is the sum of the interior angles of a triangle?

180°Triangle/Sum of interior angles

What is the sum of interior angles of a Heptagon?

900°Heptagon/Sum of interior angles

How do you find an interior angle?

In order to find the value of the interior angle of a regular polygon, the equation is (n−2)180∘n where n is the number of sides of the regular polygon.

What is the formula for a regular polygon?

You also learned the formula for finding the area of any regular polygon if you know the length of one side and the apothem: A = (n × s × a)2 A = ( n × s × a ) 2 , where n is the number of sides, s is the length of one side, and a is the apothem.

What is interior angle with example?

An angle on the interior of a plane figure. Examples: The angles labeled 1, 2, 3, 4, and 5 in the pentagon below are all interior angles. Angles 3, 4, 5, and 6 in the second example below are all interior angles as well (parallel lines cut by a transversal).

What is the Apothem of a regular polygon?

The apothem (sometimes abbreviated as apo) of a regular polygon is a line segment from the center to the midpoint of one of its sides. Equivalently, it is the line drawn from the center of the polygon that is perpendicular to one of its sides. The word “apothem” can also refer to the length of that line segment.

How many sides has a regular polygon?

Names of Regular PolygonsRegular PolygonNumber of SidesInterior AnglesEquilateral triangle3 sides3 interior angles of 60°Square4 sides4 interior angles of 90°Regular pentagon5 sides5 interior angles of 108°Regular hexagon6 sides6 interior angles of 120°2 more rows

What is the interior angle of a 6 sided polygon?

720°The General RuleShapeSidesSum of Interior AnglesQuadrilateral4360°Pentagon5540°Hexagon6720°Heptagon (or Septagon)7900°6 more rows

What do you mean by interior angles?

noun Geometry. an angle formed between parallel lines by a third line that intersects them. an angle formed within a polygon by two adjacent sides.

What is interior of an angle?

1 : the inner of the two angles formed where two sides of a polygon come together. 2 : any of the four angles formed in the area between a pair of parallel lines when a third line cuts them.

What is the sum of the interior angles of a polygon?

The sum of the measures of the interior angles of a polygon with n sides is (n – 2)180. If you count one exterior angle at each vertex, the sum of the measures of the exterior angles of a polygon is always 360°.

What is the interior angle of a 10 sided polygon?

Decagon Definitions A regular decagon has 10 equal-length sides and equal-measure interior angles. Each angle measures 144° and they all add up to 1,440° . An irregular decagon has sides and angles that are not all equal or congruent.

How many sides does a polygon have if the sum of its interior angles is 720?

6 sidesSince the figure with angles measuring 0˚ is 1 lines, then the figure with interior angles of 720˚ has 1+5=6 sides.

Why is the sum of interior angles of a polygon 180 n 2?

If you look back at the formula, you’ll see that n – 2 gives the number of triangles in the polygon, and that number is multiplied by 180, the sum of the measures of all the interior angles in a triangle. Do you see where the “n – 2” comes from? It gives us the number of triangles in the polygon.