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If a pentagon has one angle measuring 120 degrees, what can be inferred about th

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Question: If a pentagon has one angle measuring 120 degrees, what can be inferred about the other angles?

Options:

  1. All other angles must also be 120 degrees.
  2. The sum of the other angles must be 360 degrees.
  3. At least one angle must be less than 60 degrees.
  4. The pentagon cannot exist.

Correct Answer: The sum of the other angles must be 360 degrees.

Solution: 

The sum of the interior angles of a pentagon is 540 degrees. If one angle is 120 degrees, the sum of the other four angles must be 540 - 120 = 420 degrees.

If a pentagon has one angle measuring 120 degrees, what can be inferred about th

Practice Questions

Q1
If a pentagon has one angle measuring 120 degrees, what can be inferred about the other angles?
  1. All other angles must also be 120 degrees.
  2. The sum of the other angles must be 360 degrees.
  3. At least one angle must be less than 60 degrees.
  4. The pentagon cannot exist.

Questions & Step-by-Step Solutions

If a pentagon has one angle measuring 120 degrees, what can be inferred about the other angles?
  • Step 1: Understand that a pentagon has five sides and five angles.
  • Step 2: Know that the sum of all interior angles in a pentagon is 540 degrees.
  • Step 3: Identify that one angle of the pentagon is given as 120 degrees.
  • Step 4: To find the sum of the other four angles, subtract the given angle from the total sum: 540 degrees - 120 degrees.
  • Step 5: Calculate the result: 540 - 120 = 420 degrees.
  • Step 6: Conclude that the sum of the other four angles in the pentagon is 420 degrees.
  • Interior Angles of Polygons – Understanding how to calculate the sum of interior angles in polygons, specifically pentagons.
  • Angle Relationships – Recognizing how the measure of one angle affects the measures of the other angles in a polygon.
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