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Find the sum of the interior angles of a pentagon.
540 degrees
360 degrees
720 degrees
180 degrees
540 degrees
Remember the sequence for polygon sum of angles: Triangle (3 sides) = 180, Quad (4 sides) = 360, Pentagon (5 sides) = 540. Just add 180 for each additional side.
Number of sides of the polygon (pentagon), n = 5.
(n−2)×180°
Remember the sequence for polygon sum of angles: Triangle (3 sides) = 180, Quad (4 sides) = 360, Pentagon (5 sides) = 540. Just add 180 for each additional side.
Students often confuse the sum of interior angles with the sum of exterior angles, which is always 360 degrees regardless of the number of sides.
Identify the number of sides
A pentagon is a polygon with 5 sides, so n = 5.
n=5
Apply the interior angle sum formula
Use the formula for the sum of interior angles of an n-sided polygon, which is (n - 2) times 180 degrees.
(5−2)×180°
Calculate the final sum
Subtract 2 from 5 to get 3, then multiply 3 by 180 degrees.
3×180°=540°
A is correct because the sum of the interior angles of a pentagon is calculated as 540 degrees.
This formula is the basis for calculating individual interior angles of a regular polygon by dividing the sum by n, a common task in coordinate geometry and tiling problems.
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