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Anonymous asked in Science & MathematicsMathematics · 6 years ago

ABCDE is a circular pentagon.AE is the diameter of the circle.Find the value of angle ABC + angle CDE.?

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  • Pope
    Lv 7
    6 years ago
    Favorite Answer

    That would be a cyclic pentagon I believe. See the sketch below. Point O is the center, and AE is a diameter.

    angle ABC + angle CDE

    = (1/2)(arc AEC + arc CAE)

    = (1/2)[(arc AE + arc EC) + (arc CA + arc AE)]

    = (1/2)[2(arc AE) + arc EC + arc CA]

    = (1/2)[2(arc AE) + arc EA]

    = (3/2)(arc AE)

    As arc AE is a semicircle, its measure is π.

    (3/2)(arc AE) = 3π/2

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  • 6 years ago

    I know what a pentagon is but I have never heard of a circular pentagon and when I googled it I did not find out.

    The formula for the interior angles of a polygon are 180(n - 2) so the total angles are 540. A single angle would be 540/5 = 108. All angles of a regular pentagon are the same. That AE is the diameter of the circle is a red herring.

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