Interior Angles | Geometry & Measures | Maths | FuseSchool

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In this video we are going to look at the angles in polygons… the sum of all interior angles and the size of one interior angle. In another video we will look at exterior angles.

Before we start, you should already know the names of different types of polygons. If you are unsure, you may want to watch this video first.

You probably already know that if we add up all three angles in a triangle we get 180 degrees! Working from one corner, quadrilaterals can be split into two triangles. So, 180 x 2 means there are 360 degrees in any quadrilaterals.

All pentagons split into three triangles, say 180 x 3 means they have 540 degrees. What do you think the angles in octagon add up to? Pause the video. Work it out.

Octagons split into 6 triangles and so 6 x 180 means that they have 1080 degrees in all octagons.

For any polygons there are always two less triangles then there re the number of sides. So, 5 sides times 3, 6 sides times 4. We have just seen that we can easily work out the sum of interior angles, they can be regular or irregular. But to work out the size of one interior angle it has to be a regular polygon.

Regular polygon have all equal sides and angles, whereas, irregular are different. The sum of interior angles for a pentagon is 540. So, 540 divided by 5 angles is 180 degrees each.

What is the size one of one angle in a regular heptagon? Pause the video. Work it out.

Did you get 128.6 degrees?

So, here are some questions for you to do. Pause the video. Work them out and click play when you're ready.

So, there we have the interior angles of polygons, you simply need to know that there are 180 degrees in a triangle. We then look to see see how many triable fit into the polygons. There are always two less triangles than there re number of sides.

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