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In a regular pentagon, what is the measure of each interior angle?

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Question: In a regular pentagon, what is the measure of each interior angle?

Options:

  1. 108 degrees
  2. 120 degrees
  3. 90 degrees
  4. 72 degrees

Correct Answer: 108 degrees

Solution: 

The measure of each interior angle in a regular pentagon can be calculated using the formula (n-2) * 180 / n, which results in (5-2) * 180 / 5 = 108 degrees.

In a regular pentagon, what is the measure of each interior angle?

Practice Questions

Q1
In a regular pentagon, what is the measure of each interior angle?
  1. 108 degrees
  2. 120 degrees
  3. 90 degrees
  4. 72 degrees

Questions & Step-by-Step Solutions

In a regular pentagon, what is the measure of each interior angle?
  • Step 1: Identify that a regular pentagon has 5 sides (n = 5).
  • Step 2: Use the formula for calculating the measure of each interior angle: (n - 2) * 180 / n.
  • Step 3: Substitute the value of n into the formula: (5 - 2) * 180 / 5.
  • Step 4: Calculate (5 - 2) which equals 3.
  • Step 5: Multiply 3 by 180 to get 540.
  • Step 6: Divide 540 by 5 to find the measure of each interior angle: 540 / 5 = 108.
  • Step 7: Conclude that each interior angle in a regular pentagon measures 108 degrees.
  • Interior Angles of Polygons – Understanding how to calculate the measure of interior angles in regular polygons using the formula (n-2) * 180 / n.
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