Three angles of an irregular octagon are 100 degrees, 120 degrees, and 140 degrees. The remaining angles are congruent. Find the size of eac

Question

Three angles of an irregular octagon are 100 degrees, 120 degrees, and 140 degrees. The remaining angles are congruent. Find the size of each of the remaining angles

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Kinsley 6 days 2021-11-26T06:24:26+00:00 1 Answer 0

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    2021-11-26T06:25:59+00:00

    Answer:

    144°

    Step-by-step explanation:

    The sum of the interior angles of a polygon is

    sum = 180° × (n – 2) ← n is the number of sides

    Here n = 8 ( octagon ), hence

    sum = 180° × 6 = 1080°

    let the measure of 1 congruent angle be x

    Then sum the 8 angles and equate to 1080

    100 + 120 + 140 + 5x = 1080

    360 + 5x = 1080 ( subtract 360 from both sides )

    5x = 720 ( divide both sides by 5 )

    x = 144

    Thus each of the 5 congruent angles is 144°

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