My Learning Cart
?
Categories
Account

In a certain polygon, if one angle measures 120 degrees and the polygon is regul

₹0.0
Login to Download
  • 📥 Instant PDF Download
  • ♾ Lifetime Access
  • 🛡 Secure & Original Content

What’s inside this PDF?

Question: In a certain polygon, if one angle measures 120 degrees and the polygon is regular, how many sides does it have?

Options:

  1. 6
  2. 5
  3. 8
  4. 7

Correct Answer: 6

Solution: 

In a regular polygon, each interior angle can be calculated using the formula (n-2) * 180/n. Setting this equal to 120 degrees and solving for n gives n = 6, indicating a hexagon.

In a certain polygon, if one angle measures 120 degrees and the polygon is regul

Practice Questions

Q1
In a certain polygon, if one angle measures 120 degrees and the polygon is regular, how many sides does it have?
  1. 6
  2. 5
  3. 8
  4. 7

Questions & Step-by-Step Solutions

In a certain polygon, if one angle measures 120 degrees and the polygon is regular, how many sides does it have?
  • Step 1: Understand that a regular polygon has all sides and angles equal.
  • Step 2: Know the formula to find the measure of each interior angle of a regular polygon: (n-2) * 180 / n, where n is the number of sides.
  • Step 3: Set the formula equal to 120 degrees because we want to find out how many sides correspond to that angle: (n-2) * 180 / n = 120.
  • Step 4: Multiply both sides of the equation by n to eliminate the fraction: (n-2) * 180 = 120n.
  • Step 5: Distribute 180 on the left side: 180n - 360 = 120n.
  • Step 6: Move all terms involving n to one side: 180n - 120n = 360.
  • Step 7: Simplify the equation: 60n = 360.
  • Step 8: Divide both sides by 60 to solve for n: n = 360 / 60.
  • Step 9: Calculate the result: n = 6.
  • Step 10: Conclude that the polygon is a hexagon because it has 6 sides.
  • Interior Angles of Polygons – The formula for calculating the measure of each interior angle in a regular polygon, which is derived from the sum of the interior angles.
  • Regular Polygons – Understanding the properties of regular polygons, where all sides and angles are equal.
Soulshift Feedback ×

On a scale of 0–10, how likely are you to recommend The Soulshift Academy?

Not likely Very likely
Home Practice Performance eBooks