Unravel the mysterious pattern

Do you remember the angle sum of a triangle and the angle sum of a quadrilateral? Expand the sections below to discover the angle sums of other polygons.

The Pentagon is the headquarters of the United States Department of Defence, located in Arlington, Virginia. Let’s explore the angles of this image.

Open the famous pentagon activity, use the protractor to measure each of the interior angles and then find the angle sum.

Open the angle sum of a polygon activity and follow these instructions:

  • Add the angles in one of the polygons.

  • Drag the blue points and add the angles again. What do you notice?

  • Check if this is also true about the other polygons.


Copy and complete this table:

Number of sides

Angle sum (degrees)





  • What number pattern do you notice in your table?