Interior angles describe the sum of angles found within a given shape. To solve interior angle problems, you need to memorize the interior angles of two shapes: the triangle and the circle.

  • A triangle has an interior angle of 180 degrees.
  • A circle has an interior angle of 360 degrees.

The interior angles of any other polygon can be derived from these two shapes.

Example

What is the interior angle of the following shape?

interior-angles-example1

Solution

While at first glance this may seem complex, any polygon with sharp corners can be divided into triangles.

interior-angles-example2

The hexagon has now been divided into 6 triangles. Since we know each triangle has an interior angle of 180 degrees. 6 multiplied by 180 is 1080. The answer is 1080 degrees.


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