Angles in polygons

Hello, and welcome to Myriora Maths! We know the angles in a triangle add up to a hundred and eighty degrees. But what about a pentagon, or a hexagon? There's a neat trick. Let's see!

Pick one corner of the shape. Draw lines from it to all the other corners. The shape is cut into triangles!

A square cuts into two triangles. A pentagon cuts into three. A hexagon cuts into four. There are always two fewer triangles than sides.

Each triangle adds a hundred and eighty degrees. So a pentagon is three times a hundred and eighty: five hundred and forty degrees. A hexagon is four times a hundred and eighty: seven hundred and twenty degrees.

In a regular shape, all the angles are equal. So share the total. A regular hexagon has seven hundred and twenty degrees, shared between six angles: a hundred and twenty degrees each.

Let's try one together. How many triangles does an octagon cut into? Say it out loud!

An octagon has eight sides. Two fewer is six triangles. That's six times a hundred and eighty: a thousand and eighty degrees!

Here's a question that catches lots of people. How many triangles is a pentagon cut into? Some people think it's five, one for each side. But draw the lines from one corner: you only get three. The two sides next to that corner don't make their own triangles.

Your turn! What is each angle in a regular pentagon? Pick the right card. You've got twenty seconds, or pause the video. Go!

Time's up! A pentagon's angles add up to five hundred and forty degrees. Shared between five angles: a hundred and eight degrees each!

Quick review. Cut a shape into triangles from one corner. There are two fewer triangles than sides. Multiply by a hundred and eighty to find the total. In a regular shape, share the total equally. See you next time!