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Aptitude Topics

Polygons

Polygons are flat geometric shapes made of straight, connected line segments. Regular polygons have sides and angles that are all equal.

Fundamental Principles

Regular Polygon Formula

A closed shape with 'n' equal sides where all internal angles are equal and all external angles are equal.

Essential Formulation Tips

  • The exterior angles of any convex polygon always add up to exactly 360 degrees, regardless of how many sides it has.
  • At any vertex of a polygon, the interior angle and the exterior angle always add up to 180 degrees.

Shortcut Execution Techniques

  • Interior Angle Sum: The formula to find the sum of all internal angles in an n-sided polygon is: Sum = (n - 2) * 180.
  • Diagonal Count Formula: The number of unique diagonals inside an n-sided polygon can be found using: Diagonals = n * (n - 3) / 2.

Contextual Inquiries (FAQs)

Q: How do you find the measure of a single exterior angle on a regular polygon?

A: Divide 360 degrees by the total number of sides 'n' (360 / n).