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What is the measure of each interior angle of a regular pentagon?

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Question: What is the measure of each interior angle of a regular pentagon?

Options:

  1. 108 degrees
  2. 120 degrees
  3. 90 degrees
  4. 135 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 a pentagon (n=5), each angle = [(5-2) × 180] / 5 = 108 degrees.

What is the measure of each interior angle of a regular pentagon?

Practice Questions

Q1
What is the measure of each interior angle of a regular pentagon?
  1. 108 degrees
  2. 120 degrees
  3. 90 degrees
  4. 135 degrees

Questions & Step-by-Step Solutions

What is the measure of each interior angle of a regular pentagon?
  • Step 1: Identify the number of sides in a pentagon. A pentagon has 5 sides.
  • Step 2: Use the formula for finding the measure of each interior angle of a regular polygon: [(n-2) × 180] / n.
  • Step 3: Substitute the number of sides (n) into the formula. For a pentagon, n = 5.
  • Step 4: Calculate (n-2). This is 5 - 2 = 3.
  • Step 5: Multiply the result from Step 4 by 180. This is 3 × 180 = 540.
  • Step 6: Divide the result from Step 5 by the number of sides (n). This is 540 / 5 = 108.
  • Step 7: Conclude that each interior angle of a regular pentagon measures 108 degrees.
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