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16 June, 17:49

West High School has a math building in the shape of a regular octagon. When Mrs. Woods measures an interior angle of the octagon (which is inside her classroom), she gets 135°.

Mrs. Wood's ceiling is 10.0 feet high and the length of one side of the building is 25.0 feet. What is the volume of West High School's math building?

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Answers (1)
  1. 16 June, 18:27
    0
    8 sides

    The building is an octagon

    Step-by-step explanation:

    The sum of all the interior angles in a polygon can be found by the equation

    S

    =

    180

    (

    n

    -

    2

    )

    where

    n

    is the number of sides the polygon has.

    We know that one interior angle is

    135

    degrees and that all the interior angles are the same because this is a regular polygon. So the sum of the angles must be

    135

    n

    (

    135

    degrees times the number of sides, or the number of angles).

    135

    n

    =

    180

    (

    n

    -

    2

    )

    135

    n

    =

    180

    n

    -

    360

    135

    n

    +

    360

    =

    180

    n

    45

    n

    =

    360

    n

    =

    8



    There are

    8

    sides and

    8

    interior angles of

    135

    degrees
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