### You may remember that for all triangles the interior angle sum is always 180°, but what about a pentagon, or a hexagon? What about the sum of all the exterior angles? Is there a way of figuring out this? A formula?

### The answer for all those questions is carefully presented in this lesson. You will study the proof to obtain the general formula for interior, and for exterior angle sum. We are going to solve multiple examples, and you will have the choice of solving some on your own in the slides provided for that purpose and in which you will be able to write the proof with your stylus and pulling down the marker tools menu at the top of the screen. Surely you will get invigorated with this lesson!

** Lesson's Content **

** Lesson's Glossary **

**Angle **

Geometry shape formed by two rays (initial and ending sides of the angle) that share a common endpoint called the vertex. You may name an angle using the vertex, or a point in each ray and the vertex label in the center.

**Concave polygon**

If a polygon has diagonals that lie outside the polygon then the polygon is concave.

Convex polygon

A convex polygon is any polygon that is not concave.

**Decagon **

A ten-sided polygon.

**Dodecagon **

A twelve-sided polygon.

**Heptagon **

A seven-sided polygon.

Hexagon

A six-sided polygon.

irregular polygon

An irregular polygon is any polygon that is not regular.

**N-gon **

A polygon with n sides.

**Nonagon **

A nine-sided polygon.

**Octagon **

An eight-sided polygon.

**Pentadecagon **

A 15-sided polygon.

Pentagon

A five-sided polygon.

** Polygon**

A polygon is a two-dimensional geometric figure with these characteristics: •

It is made of straight line segments.

Each segment touches exactly two other segments, one at each of its endpoints.

It is closed -- it divides the plane into two distinct regions, one inside and the other outside the polygon.

Regular polygon

A regular polygon has sides that are all the same length and angles that are all the same size.

**Quadrilateral **

A four-sided polygon.

**Septagon **

A seven-sided polygon.

**Side of a polygon **

- a single segment from the union that forms a polygon.

**Vertex of a polygon **

An endpoint of a segment in a polygon.

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