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If a polygon has 8 sides, what is the measure of each interior angle in a regula

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Question: If a polygon has 8 sides, what is the measure of each interior angle in a regular octagon?

Options:

  1. 135 degrees
  2. 120 degrees
  3. 108 degrees
  4. 150 degrees

Correct Answer: 108 degrees

Solution: 

The measure of each interior angle of a regular polygon can be calculated using the formula [(n-2) * 180] / n. For an octagon (n=8), it is [(8-2) * 180] / 8 = 135 degrees.

If a polygon has 8 sides, what is the measure of each interior angle in a regula

Practice Questions

Q1
If a polygon has 8 sides, what is the measure of each interior angle in a regular octagon?
  1. 135 degrees
  2. 120 degrees
  3. 108 degrees
  4. 150 degrees

Questions & Step-by-Step Solutions

If a polygon has 8 sides, what is the measure of each interior angle in a regular octagon?
  • Step 1: Identify the number of sides in the polygon. For an octagon, n = 8.
  • Step 2: Use the formula for calculating the measure of each interior angle of a regular polygon: [(n-2) * 180] / n.
  • Step 3: Substitute the value of n into the formula: [(8-2) * 180] / 8.
  • Step 4: Calculate (8-2) which equals 6.
  • Step 5: Multiply 6 by 180 to get 1080.
  • Step 6: Divide 1080 by 8 to find the measure of each interior angle: 1080 / 8 = 135.
  • Step 7: Conclude that each interior angle in a regular octagon measures 135 degrees.
  • Interior Angles of Polygons – Understanding how to calculate the measure of interior angles in regular polygons using the formula.
  • Regular Polygons – Recognizing the properties of regular polygons, where all sides and angles are equal.
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