What is the sum of the measures of the interior angles of a convex octagon?
What is the sum of the measures of the interior angles of a convex decagon?
What is the measure of one interior angle of a regular polygon with 20 sides?
Thank You! (:
To find the sum of the measures of the interior angles of a convex polygon, you can use the formula:
Sum = (n - 2) * 180 degrees
where "n" represents the number of sides of the polygon.
1. For a convex octagon (a polygon with 8 sides), substitute "n" with 8 in the formula:
Sum = (8 - 2) * 180 degrees
= 6 * 180 degrees
= 1080 degrees
Therefore, the sum of the measures of the interior angles of a convex octagon is 1080 degrees.
2. For a convex decagon (a polygon with 10 sides), substitute "n" with 10 in the formula:
Sum = (10 - 2) * 180 degrees
= 8 * 180 degrees
= 1440 degrees
Therefore, the sum of the measures of the interior angles of a convex decagon is 1440 degrees.
3. For a regular polygon with 20 sides, all interior angles are equal. To find the measure of one interior angle, divide the sum by the number of sides:
Measure of one interior angle = Sum / n
= (n - 2) * 180 degrees / n
= (20 - 2) * 180 degrees / 20
= 18 * 180 degrees / 20
= 162 degrees
Therefore, the measure of one interior angle of a regular polygon with 20 sides is 162 degrees.