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Interior Angles of Polygons

source : mathsisfun.com

Interior Angles of Polygons

An Interior Angle is an angle inside a shape

Another example:

Triangles

The Interior Angles of a Triangle add up to 180°

Let’s try a triangle:90° + 60° + 30° = 180°

It works for this triangle

Now tilt a line by 10°:80° + 70° + 30° = 180°

It still works!One angle went up by 10°,and the other went down by 10°

Quadrilaterals (Squares, etc)

(A Quadrilateral has 4 straight sides)

Let’s try a square:90° + 90° + 90° + 90° = 360°

A Square adds up to 360°

Now tilt a line by 10°:80° + 100° + 90° + 90° = 360°

It still adds up to 360°

The Interior Angles of a Quadrilateral add up to 360°

Because there are 2 triangles in a square …

The interior angles in a triangle add up to 180° …

… and for the square they add up to 360° …

… because the square can be made from two triangles!

Pentagon

A pentagon has 5 sides, and can be made from three triangles, so you know what …

… its interior angles add up to 3 × 180° = 540°

And when it is regular (all angles the same), then each angle is 540° / 5 = 108°

(Exercise: make sure each triangle here adds up to 180°, and check that the pentagon’s interior angles add up to 540°)

The Interior Angles of a Pentagon add up to 540°

The General Rule

Each time we add a side (triangle to quadrilateral, quadrilateral to pentagon, etc), we add another 180° to the total:

So the general rule is:

Sum of Interior Angles = (n−2) × 180°

Each Angle (of a Regular Polygon) = (n−2) × 180° / n

Perhaps an example will help:

Example: What about a Regular Decagon (10 sides) ?

Sum of Interior Angles = (n−2) × 180°

 = (10−2) × 180°

 = 8 × 180°

 = 1440°

And for a Regular Decagon:

Each interior angle = 1440°/10 = 144°

Note: Interior Angles are sometimes called “Internal Angles”

 

An interior angle of a regular polygon has a measure of 108°. What...

An interior angle of a regular polygon has a measure of 108°. What… – Where n is the number of sides of the polygon, According to the question ⇒ It is a pentagon.Polygons – Pentagons – Cool Math has free online cool math lessons, cool math games and fun math activities. Really clear math lessons (pre-algebra, algebra, precalculus), cool math games, online graphing calculators To find the sum of the interior angles of a pentagon, divide it up into triangles…An interior angle of a regular polygon has a measure of 108°. What type of polygon is it? It is a convex pentagon because it has five sides and none of the sides would extend into the inside of the polygon.

Polygons – Pentagons – Polygons come in two broad categories—regular and irregular. A regular polygon has all equal Irregular Polygons. A polygon will always have the same number of sides as it has angles. So a polygon with nine sides will have nine angles. The different types of polygons are named after their…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. For example the interior angles of a pentagon always add up to 540° no matter if it regular or irregular, convex or concave, or what size and shape it is.The exterior and the interior angles add up to 180º. To find the exterior angle you subtract 108º from 180º. This polygon is a pentagon as it has 5 sides.

Polygons - Pentagons

Angle Measures of Polygons Assignment and Quiz Flashcards | Quizlet – A regular polygon is a polygon whose sides are of equal length. Examples for regular polygon are Though the sum of interior angles of a regular polygon and irregular polygon with the same number In case of regular polygons, the measure of each interior angle is congruent to the other….of interior angles of a polygon under the topic Polygons of the section Geometry in this site. Find the fifth interior angle of a convex pentagon if it has four interior angles of 75°, 85°, 115° ° = 540°. In the regular pentagon, all interior angles are congruent, hence, have the same angle measure.A regular polygon is equiangular. All of its angles have the same measure. It is also equilateral. A square is a regular polygon, and while a square is a type of rectangle, rectangles which are not Example 5. If the measure of each interior angle of a regular polygon is 150, find the number of…

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