Now let’s explore the sum of the 4 angles in any quadrilateral.

Any convex quadrilateral can be split into 2 triangles.

If each triangle consists of 180, then 2 triangles would total 360.

This can easily be seen in the square. 90 + 90 + 90 + 90 = 360 90 90 90 90

Any convex pentagon can be split into 3 triangles.

Each triangle consists of 180.

180 + 180 + 180 = 540 180 180 180

Now let’s chart our findings. Polygon Sum of all angles triangle 180 quadrilateral 360 pentagon 540

Do you notice any pattern? Polygon Sum of all angles triangle 180 quadrilateral 360 pentagon 540

As the number of sides on the polygons increase by 1 side, the sum of the angles increases by 180.  Sum of all angles triangle 180 quadrilateral 360 pentagon 540 + 180 + 180

What is the sum of all angles in a convex hexagon?

hexagon Polygon Sum of all angles triangle 180 quadrilateral 360 pentagon 540 hexagon

hexagon 720 Polygon Sum of all angles triangle 180 quadrilateral 360 pentagon 540 hexagon 720