Question

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5. For a regular octagon:

a. Find the measure of a single interior octagon angle.

b. Find the measure of a single exterior octagon angle.

Answer 1

a. 135°

b. 45°

Explanation:

a.

To find the measure of a single interior angle of a regular octagon, we can use the formula:

Interior angle = (n-2) x 180 / n

where n is the number of sides of the regular polygon. For an octagon, n = 8, so we have:

Interior angle = (8-2) x 180 / 8 = 135 degrees

Therefore, each interior angle of a regular octagon measures 135 degrees.

b. The sum of the measures of the exterior angles of any polygon is always 360 degrees. Since a regular octagon has eight sides, it also has eight exterior angles. To find the measure of a single exterior angle of a regular octagon, we can divide the sum of the measures of the exterior angles by the number of exterior angles, which gives:

360 degrees / 8 = 45 degrees

Therefore, each exterior angle of a regular octagon measures 45 degrees.

Answer 2

• A) 135°; B) 45°.

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Octagon has 8 sides and 8 angles.

Sum of interior angles:

• S = 180°(n - 2) = 180°(8 - 2) = 180°(6) = 1080°

Part A

Each interior angle measure is:

• S/n = 1080°/8 = 135°

Part B

Each exterior angle is the supplementary with interior angle, so its measure is:

• 180° - 135° = 45°