Table of Contents

- 1 How many sides does a regular polygon have if one interior angle measures 135?
- 2 What polygon will tessellate by itself?
- 3 What must be true about the measure of an interior angle of a regular polygon in order for the polygon to tessellate?
- 4 How are the polygons arranged in a regular tessellation?
- 5 What is the sum of the angles of a polygon?

## How many sides does a regular polygon have if one interior angle measures 135?

8

Complete step-by-step answer: we have to find the number of sides of the polygon. Let’s start with the assumption that the number of sides be n, this means that we have n sided regular polygon whose interior angle is 135∘. Therefore, we get the number of sides that the polygon has as 8.

## What polygon will tessellate by itself?

Only three regular polygons (shapes with all sides and angles equal) can form a tessellation by themselves—triangles, squares, and hexagons.

**Is it possible for a regular polygon to have an interior angle measure of 130 explain?**

The number of sides has to be a natural number, so 7.2 is not possible, therefore 130° is not possible for the angles of a regular polygon.

**How many sides does a regular polygon have if each of its interior angles is 165?**

24

Hence the number of sides a regular polygon has if its interior angle is 165 degrees are 24.

### What must be true about the measure of an interior angle of a regular polygon in order for the polygon to tessellate?

A regular polygon can only tessellate the plane when its interior angle (in degrees) divides 360 (this is because an integral number of them must meet at a vertex). This condition is met for equilateral triangles, squares, and regular hexagons.

### How are the polygons arranged in a regular tessellation?

With both regular and semi-regular tessellations, the arrangement of polygons around every vertex point must be identical. This arrangement identifies the tessellation. For example, a regular tessellation made of hexagons would have a vertex configuration of {6, 6, 6} because three hexagons surround any random vertex.

**How to calculate the interior angle of a polygon?**

In order to find the measure of a single interior angle of a regular polygon (a polygon with sides of equal length and angles of equal measure) with n sides, we calculate the sum interior angles or and then divide that sum by the number of sides or .

**What kind of polygons have less than 180 degrees?**

We’ll stick with “convex” polygons, those whose interior angles are each less than 180 degrees, and we’ll allow ourselves to move them around, rotate them and flip them over. But we won’t assume the side lengths and interior angles are all the same.

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

So it is pentagon. The sum of the measures of the exterior angles of a convex polygon, one angle at each vertex is = 360° We can add the measures of all exterior angles of the above pentagon and the sum can be equated to 360°.