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Is there a relationship between a polygon's number of sides and its number of vertices and angles?
For a regular polygon, all sides are equal and all angles are equal. Draw a regular hexagon. This website shows you an easy way to draw a hexagon with a compass. http://www.wikihow.com/Draw-a-Hexagon
Draw a line from one vertex to another going thru the center. This should make 2 identical triangles. Do this, until you have 6 triangles. Use a protractor to measure the 6 angles in the center and the base angles. They should each be 60º angles. Two of these adjacent base angles measure 120º. This is the vertex angle. There are 6 vertices, 6 sides, 6 - 60º angles in the center, and 6 - 120º angles at the 6 vertices.
1. If a polygon has n sides, there will be n angles at the center, n vertices and n triangles.
2. Draw the 5 lines connecting each vertex to the center of the polygon making 5 angles.
- There are 360º around the center point, so 360º ÷ n is the measure of each angle at the center.
- The angle of the triangle at the center of the polygon = 360 º ÷ n. This angle is the angle of the triangle at the center of the polygon.
- The sum of the interior angles in a triangle = 180º
- The sum of the 2 base angles of each triangle must be 180 º - (360 º÷ n).
- Each of the base angles of the triangle must measure (180º - (360 º÷ n)) ÷ 2.
- Two adjacent base triangles from adjacent triangles form a vertex angle, so the vertex angle = 2* (180º - (360 º÷ n)) ÷ 2.
Two adjacent base angles = one vertex angle.
The vertex angle = 2 * (180º - (360 º÷ n) ÷ 2, which means you do not have to divide by 2. You can stop at step #6.
Now let's try a sample problem. Here is a site for constructing a pentagon. http://www.kjmaclean.com/Geometry/PentConstruct.html
Find the relationship between a pentagon's number of sides and its number of vertices and angles? Since a penta means 5, a pentagon has 5 sides, 5 vertices, and 5 angles. Now let's find the vertex angle.
- Since a penta means 5, a pentagon has 5 sides, 5 vertices, and 5 angles.
- 5 angles
- 360º ÷ 5 = 72º
- The angle of the triangle at the center of the polygon = 72º
- 72 º + nº + nº = 180º
- 180 º - (360 º÷ 5) = 108º
- Each of the base angles of the triangle must measure 108º ÷ 2 = 54 º
- The vertex angle = 2* 54 º = 108º
- Notice that the answer to #6 and #8 are the same.
What else can I help you with?
Are polygons whose vertices can be paired so that corresponding angles are congruent and corresponding sides are proportional?
The fact that corresponding angles are congruent does not require corresponding sides to be proportional - except in the case of a triangle. For quadrilaterals, think of a square and rectangle.
What is the sum of the measure of the exterior angles of a nonagon?
As for all polygons the exterior angles add up to 360 degrees
How do you work out the sum of exterior angles for a pentagon?
all regular polygons (such as a pentagon) have the sum of their exterior angles = 360 degrees
What is Sum of all exterior angles of a triangle?
360 degrees as is with all other polygons!
How can you tell whether two polygons are similar?
Polygons will be similar if they have the same number of sides AND all of their angles are the same. All of their angles are the same if all but one of their angles are the same because with the same number of sides the angles must add up to the same thing. All squares are similar (4 right angles and sides of equal lenght). All rectangles are similar (4 right angles). We know two triangle are similar if two or mare angles are the same, or if one angle is the same and the two adjacent sides are the same length. Variations of this last proof may apply to some other polygons.
What is a vertex in angles?
It is the singular of the plural vertices relating to angles of polygons
Does a polygonn usually have more sides or more angles explain?
Polygons always have the same amount of sides and angles, as if you have, for example, 4 sides, you will have 4 vertices, and 4 vertices means 4 angles.
What is the relationship between the interior and exterior angles in polygons?
An interior angle and the corresponding exterior angle add up to a straight angle. that is, they are supplementary.
What is the difference between angles and vertices?
Angles are measured by degree and vertices happen when two sides meet, and aren't measured.
How many faces edges vertices does a polygon have?
Ah, polygons are like little friends with different personalities! The number of faces, edges, and vertices a polygon has depends on its shape. For example, a triangle has 3 sides, 3 vertices, and 3 angles. Remember, each polygon is unique and beautiful in its own way!
What is the difference between angles and vertices's in math?
Angles are the degree measure between the two rays that make an angle. Vertices are the point in which the two rays meet to create that angle.
How are the polygons in the mosaic alike and different?
The polygons in the mosaic are alike in that they share common characteristics such as having straight edges and defined vertices. However, they differ in terms of their shapes, sizes, and angles; some may be regular polygons with equal sides and angles, while others are irregular. Additionally, the arrangement and color patterns of the polygons can vary, affecting the overall visual impact of the mosaic.
Do all polygons have congruent angles?
No only regular polygons have congruent angles.
Which figures have the same number of sides vertices and angles?
Vertices and angles are the same thing. Any polygon has an equal number of sides and vertices (and, therefore, angles).Vertices and angles are the same thing. Any polygon has an equal number of sides and vertices (and, therefore, angles).Vertices and angles are the same thing. Any polygon has an equal number of sides and vertices (and, therefore, angles).Vertices and angles are the same thing. Any polygon has an equal number of sides and vertices (and, therefore, angles).
How do you classify quadrilateral?
You classify a quadrilateral by its sides, angles, and its vertices. All quadrilaterals are 4-sided polygons having 4 interior angles that add up to 360 degrees.
How many angles does a regular dodecagon have?
It has 20 vertices or angles. * * * * * No! A dodecagon has 12 vertices. A polygon with 20 vertices is an icosagon.
What are convex polygons with congruent sides and congruent angles?
Convex polygons with congruent sides and congruent angles are called regular polygons.
