# What is the sum of the measures of the exterior angles of any convex polygon apex?

Table of Contents

## What is the sum of the measures of the exterior angles of any convex polygon apex?

Exterior Angle Sum Theorem states that the exterior angles of any polygon will always add up to 360 degrees.

## What is the sum of the exterior angles of a convex polygon with N sides?

Conjecture (Exterior Angle Conjecture ): The sum of the n exterior angles for any convex polygon with n sides is 360 degrees.

## What is the formula for finding the sum of the angles of any convex polygon?

Theorem 39: If a convex polygon has n sides, then its interior angle sum is given by the following equation: S = ( n −2) × 180°. Theorem 40: If a polygon is convex, then the sum of the degree measures of the exterior angles, one at each vertex, is 360°.

## Why is the sum of the exterior angles of any convex polygon always equal 360?

Summed, the exterior angles equal 360 degreEs. A special rule exists for regular polygons: because they are equiangular, the exterior angles are also congruent, so the measure of any given exterior angle is 360/n degrees. That is why they are supplementary–because their measures sum to 180 degrees instead of 360.

## What is the sum of the interior angles of a 36 sided polygon?

In geometry, a triacontagon or 30-gon is a thirty-sided polygon. The sum of any triacontagon’s interior angles is 5040 degrees….Triacontagon.

Regular triacontagon | |
---|---|

Symmetry group | Dihedral (D30), order 2×30 |

Internal angle (degrees) | 168° |

Dual polygon | Self |

## What is the sum of the measure of the interior angles of a 13-sided polygon?

For a pentagon, it’s (5-2)180=(3)180=540 degrees. So plug in n=13 to see the sum of the angle measures for a 13-sided polygon.

## What is the measure of an exterior angle of a regular 13 sided polygon?

Thus our interior angle = 152.3 and exterior angle =27.7. You can check this answer as the sum of all exterior angles equates to 360 degrees.

## What is the measure of one exterior angle of a regular pentagon?

Answer: The measure of each exterior angle of a regular pentagon is 72° A regular pentagon has all angles of the same measure and all sides of the same length.

## What is the sum of the interior angles of a 18 sided polygon?

The sum of the measures of the interior angle of any polygon is the number of sides minus 2 multiplied by 180. A polygon with 18 sides has an interior angle sum of 2880 degrees.

## What is the sum of the measures of the interior angles of a 5 sided convex polygon?

The General Rule

Shape | Sides | Sum of Interior Angles |
---|---|---|

Triangle | 3 | 180° |

Quadrilateral | 4 | 360° |

Pentagon | 5 | 540° |

Hexagon | 6 | 720° |