Question

If the sum of the interior angles of a regular polygon measures up to 144 degrees, how many sides does the polygon have?

• A. 8
• B. 10
• C. 12
• D. 9

Answer 1

Answer:

B. 10

Mathematics - Solids

• The sum of the interior angles of a polygon with 'n' sides is given by the formula: (n-2) * 180 degrees.
• In this problem, the sum of the interior angles is given as 1440 degrees.
• We can set up an equation using the formula: (n-2) * 180 = 1440.
• To find the number of sides 'n', we first divide both sides of the equation by 180: n-2 = 1440 / 180.
• Calculating the division: n-2 = 8.
• Finally, we add 2 to both sides to solve for 'n': n = 8 + 2.
• Therefore, the polygon has 10 sides.
• Key Concept for Exams: A regular polygon has all sides equal and all interior angles equal. The formula for the measure of each interior angle of a regular polygon is ((n-2) * 180) / n.
• Example: If a regular polygon has 3 sides (a triangle), the sum of interior angles is (3-2)*180 = 180 degrees. Each angle is 180/3 = 60 degrees.
• Example: If a regular polygon has 4 sides (a square), the sum of interior angles is (4-2)*180 = 360 degrees. Each angle is 360/4 = 90 degrees.