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The measure of a single interior angle in a regular octagon is (4x + 12)0. Find the value of x, rounding your answer to the nearest tenth.

User Tyler
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1 Answer

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24 votes

Answer:

x ≈ 30.8

Explanation:

You want the value of x if the measure of an interior angle of a regular octagon is (4x +12)°.

Interior angles

The sum of interior angles of an n-gon is 180°×(n -2), where n is the number of sides. An octagon has 8 sides, so the sum of angles is ...

180°×(8 -2) = 1080°

The angles of a regular n-gon are congruent, so one interior angle of a regular octagon is ...

1080°/8 = 135°

Application

The given angle expression is equal to 135°, so we have ...

(4x +12)° = 135°

4x = 123 . . . . . . . divide by ° and subtract 12

x = 30.75 . . . . . . divide by the coefficient of x

The value of x is about 30.8.

User Katie Byers
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