Interior and Exterior Angles in Polygons — Practice Geometry Questions

By Allen Ma, Amber Kuang

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

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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.

  1. Solve for x.

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  2. Solve for x.

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Answers and explanations

  1. 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

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    The pentagon is missing one interior angle, which you can call y:

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    The interior and exterior angles of a polygon are supplementary. Therefore,

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  2. 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

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    Add the interior angles, set the sum equal to 720, and solve for x:

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