Interior angles in polygons — Gateways School

LO: Use the sum of the interior angles in a polygon

Some definitions we need to know:

A polygon is any closed 2D shape with straight sides

A diagonal is a line from one vertex (corner) of a polygon to another

Names of some common polygons:

In a regular polygon all the sides and interior angles are the same:

We already know that the interior (inside) angles of a triangle ALWAYS add up to 180^o

The interior angles of a quadrilateral add up to 2 x 180 = 360^o because a quadrilateral can be split into 2 triangles

We can work out the sum of the interior angles (what they add up to) for a pentagon by splitting it into triangles:

Use this idea to fill in the table below - then check at the bottom of the page to see if you were right:

In general, we take away 2 from the number of sides to get the number of triangles and then multiply by 180...

Sum of interior angles for n sided shape = (n-2)x180

Once we know the sum of the interior angles for a polygon we can use this to find any missing angles:

Example

Use the rest of the lesson to see how many missing angles you can find for question 11 below. You may use a calculator but show what you are typing in - working could be set out as in the example above. Before the end of the lesson mark your answers (bottom of page), take a photo of your marked work and upload in Firefly.

ANSWERS: