In geometry, you can find the sum of the interior or exterior angles of a polygon based on the number of sides the polygon has. You can then apply this information to find individual interior or exterior angles.
The sum of the exterior angles of any polygon is 360 degrees. The formula
tells you the sum of the interior angles of a polygon, where n represents the number of sides.
Practice questions
Use your knowledge of the sums of the interior and exterior angles of a polygon to answer the following questions.
Solve for x.
Solve for x.
Answers and explanations
58 degrees
The sum of the exterior angles of a polygon is 180 (n – 2), where n represents the number of sides. The sum of the angles of a pentagon (five sides) is equal to
The pentagon is missing one interior angle, which you can call y:
The interior and exterior angles of a polygon are supplementary. Therefore,
20 degrees
The sum of the interior angles of a polygon is 180 (n – 2), where n represents the number of sides. The sum of the angles of a hexagon (six sides) is equal to
Add the interior angles, set the sum equal to 720, and solve for x:
