## the sum of the measures of the interior angles of a convex polygon is given find the number of sides your your solution

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the sum of the measures of the interior angles of a convex polygon is given find the number of sides your your solution

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1. Finding the Sum of the Interior Angle Measures of a Convex Polygon Given the Number of Sides
Step 1: Count the number of sides on the polygon. Call this number
n
.
Step 2: Calculate the sum of the interior angle measures using the formula
S
=
180
(
n
2
)
. The result is the sum of the interior angle measures in degrees.
Finding the Sum of the Interior Angle Measures of a Convex Polygon Given the Number of Sides: Vocabulary and Equations
Convex Polygon: A convex polygon is a two-dimensional shape made with straight edges, such that each interior angle measure is less than
180
.
Interior Angle: An interior angle of a polygon is an angle that is created where the sides of the polygon meet and is inside the boundaries of the polygon.
Sum of the Interior Angle Measures of a Convex Polygon: The sum of the interior angle measures of a convex polygon is given by the formula:
S
=
(
180
(
n
2
)
)
Where
n
is the number of sides of the polygon.
We will use these steps, definitions, and equations to find the sum of the interior angle measures of a convex polygon in the following two examples.
Finding the Sum of the Interior Angle Measures of a Convex Polygon Given the Number of Sides: Example Problem 1
Find the sum of the interior angles of the polygon shown in the image below.
Polygon for Example 1
Polygon for Example 1
Step 1: Count the number of sides on the polygon. Call this number
n
.
Counting the Sides
Counting the Sides
We see that there are 6 sides on this polygon, so we have
n
=
6
.
Step 2: Calculate the sum of the interior angle measures using the formula
S
=
180
(
n
2
)
. The result is the sum of the interior angle measures in degrees.
Since
n
=
6
, we have:
S
=
180
(
n
2
)
=
180
(
6
2
)
=
180
(
4
)
=
720