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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Bea44 2022-07-26T18:05:44+00:00 1 Answer 0

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    2022-07-26T18:06:54+00:00
    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

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