Angles in a polygon

Pick one corner of the 10-sided shape and draw a line from it to every corner it is not already joined to — the shape splits into triangles.

That corner reaches every other corner except its two neighbors, so a 10-sided shape splits into 10 − 2 = 8 triangles.

Every triangle's angles add to 180°, and together they make up all the angles of the shape: 8 × 180 = 1440°.

The shape is regular, so every angle is the same. 1440 shared between 10 is 1440 ÷ 10 = 144°.

So each angle of a regular 10-sided shape is 144°.