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Laabri

Interior Angle Sums in Polygons

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Last updated over 4 years ago
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Please complete each of the below examples to the best of your ability.

Use one of the following two strategies for determining the interior angle sum for a polygon:

1) Draw diagonals to create triangles, which have an interior angle sum of 180⁰. In the blue pentagon below, two diagonals create three triangles → 180 • 3 = 540⁰ interior angle sum

2) Use the formula method >>> (n − 2) • 180, where n = the number of the sides. The blue quadrilateral below has four sides. Substitute 4 in for n → (4 − 2) • 180 = 360⁰ interior angle sum

You can also use your notes and/or the following videos for assistance as needed.

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1.

Find the measure of the fourth interior angle.

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2.

The figure below displays a hexagon. What is the measure of angle x?

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3.

Using a method of your choice, determine the sum of the interior angles within this regular nonagon.

Please type just the number!

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4.

Using a method of your choice, determine the sum of the interior angles within this regular heptagon.

Please type just the number!

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5.

Using a method of your choice, determine the sum of the interior angles within this irregular hexagon. Then, solve for the measure of angle x.

Please type just the number!

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6.

Using a method of your choice, determine the sum of the interior angles within this irregular heptagon. Then, solve for x.

Please type just the number!

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7.

Determine the measure of each individual interior angle in a regular hexagon (six-sided figure).

Please type just the number!

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8.

Determine the measure of each individual interior angle in a regular dodecagon (12-sided figure).

Please type just the number!

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9.

Find the number of sides in a polygon whose sum of the interior angles is 1800.

Please type just the number!

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10.

The border of a Susan B. Anthony dollar is in the shape of a regular polygon.

a) The polygon has sides.

b) The measure of each interior angle of the border is degrees. Round your answer to the nearest degree!