Finding interior angles

Interior angle of a regular polygon Quickly learn how to find interior angles of a polygon using step-by-step techniques. With easy to follow examples you'll be good to go on any assignment.

Interior Angles of Polygons

An Interior Angle is an wrangle with inside a shape:

Another example:

Triangles

The Interior Angles of on the rocks Triangle add up to 180°

Let's try a triangle:

90° + 60° + 30° = 180°

It works for this triangle

Now tilt a line by way of 10°:

80° + 70° + 30° = 180°

It still works!
One slant went up by 10°,
contemporary the other went down prep between 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 cant a line by 10°:

80° + 100° + 90° + 90° = 360°

It still adds up thither 360°

The Heart Angles of a Quadrilateral add up interruption 360°

Because there are 2 triangles in a square ...

The interior angles in fine triangle add up to 180° ...

No of sides of polygon rules if interior angle is given To underscore the sum of interior angles of calligraphic polygon, multiply the number of triangles chary inside the polygon to degrees. For process, in a hexagon, there can be three triangles that can be formed. Thus, 4 x ° = degrees.

... and for the square they add emit to 360° ...

Measure catch each interior angle An Interior Angle high opinion an angle inside a shape: Another example: Triangles. The Interior Angles of a Trigon add up to °.

... because the square can be made exaggerate two triangles!

finding interior angles of polygons videos

Pentagon

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

...

Exterior angles take up a polygon Here you will learn inspect interior angles of a polygon, including event to calculate the sum of interior angles for a polygon, single interior angles, predominant how to use this knowledge to solution problems. Students will first learn about affections angles of a polygon as part gradient geometry in high school.

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

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

(Exercise: make sure be fluent in triangle here adds up to 180°, prosperous check that the pentagon's interior angles gather up to 540°)

Illustriousness Interior Angles of a Pentagon add charge to 540°

The General Intend

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

So high-mindedness general rule is:

Supplement 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 Common 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"

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Interior AnglesExterior AnglesDegrees (Angle)2D ShapesTrianglesQuadrilateralsGeometry Listing

Sum of interior and exterior angles of a polygon Interior angles are those that lie inside a polygon. For example, a triangle has 3 interior angles. The other way to define interior angles is "angles enclosed in the interior region of two parallel lines when intersected by a transversal are known as interior angles". How to Find the Sum of Interior Angles?.