If the sum of the interior angles of a regular polygon measures 1440o, how many sides does the ...
If the sum of the interior angles of a regular polygon measures 1440o, how many sides does the polygon have?
Answer/Solution
10 sides
Steps/Work
Explanatory Answer
Step 1: Compute sum of all interior and exterior angles
The sum of an exterior angle and an interior angle of a polygon = 180o.
The sum of all the exterior angles of a polygon = 360o.
From the question stem: sum of all interior angles of the given polygon = 1440o.
Therefore, sum of all the interior and all exterior angles of the polygon = 1440 + 360 = 1800o.
Step 2: Compute number of sides
If there are 'n' sides to this polygon, then the sum of all the exterior and interior angles = 180 * n = 1800o.
Therefore, n = 10.
Alternative Approach : Using formula
Sum of all interior angles of a convex polygon = (n - 2)* 180
So, (n - 2) * 180 = 1440
n - 2 = 8
n = 10
Choice A
Step 1: Compute sum of all interior and exterior angles
The sum of an exterior angle and an interior angle of a polygon = 180o.
The sum of all the exterior angles of a polygon = 360o.
From the question stem: sum of all interior angles of the given polygon = 1440o.
Therefore, sum of all the interior and all exterior angles of the polygon = 1440 + 360 = 1800o.
Step 2: Compute number of sides
If there are 'n' sides to this polygon, then the sum of all the exterior and interior angles = 180 * n = 1800o.
Therefore, n = 10.
Alternative Approach : Using formula
Sum of all interior angles of a convex polygon = (n - 2)* 180
So, (n - 2) * 180 = 1440
n - 2 = 8
n = 10
Choice A