Geometry: 1,001 Practice Problems For Dummies (+ Free Online Practice)
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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

    image3.png

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

    image4.png

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

    image5.png
  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

    image6.png

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

    image7.png

About This Article

This article is from the book:

About the book authors:

Allen Ma and Amber Kuang are math teachers at John F. Kennedy High School in Bellmore, New York. Allen, who has taught geometry for 20 years, is the math team coach and a former honors math research coordinator. Amber has taught all levels of mathematics, from algebra to calculus, for the past 14 years.

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