Engineering Board Exam Reviewer · Polygons · medium

A polygon has 54 diagonals. How many sides does it have?

  1. 9
  2. 10
  3. 12
  4. 15

Answer

C. 12

Solution

n(n-3)/2=54 n2-3n-108=0 (n-12)(n+9)=0, so n=12.

More Polygons questions

  1. Each interior angle of a regular polygon measures 150°. How many sides does it have?
  2. How many diagonals does a decagon have?
  3. Find the measure of each exterior angle of a regular octagon.
  4. Find the sum of the interior angles of a hexagon.
  5. Find the sum of the interior angles of a 12-sided polygon (dodecagon).
  6. Find the measure of each interior angle of a regular nonagon (9 sides).
  7. How many sides does a regular polygon have if each exterior angle measures 24°?
  8. Find the number of diagonals in a regular polygon with 15 sides.
  9. The sum of the interior angles of a polygon is 1980°. How many sides does it have?
  10. Find the area of a regular hexagon with side length 8 cm.

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