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16 January, 14:35

Threeangles of a quadrilateral are equal and its fourth angel is 120°. Find all the angels

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  1. 16 January, 15:23
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    Each of the three congruent angles has measure 80 deg. The fourth angle has measure 120 deg.

    Step-by-step explanation:

    The sum of the measures of the angles of an n-sided polygon is (n - 2) 180.

    A quadrilateral has 4 sides, so n = 4 in the formula above.

    (n - 2) 180 = (4 - 2) 180 = 2 (180) = 360

    The sum of the measures of the angles of a quadrilateral is 360 degrees.

    Three angles are congruent. Let the measures of the three congruent angles be x. The sum of the measures of the 3 angles is x + x + x = 3x.

    The sum of the measures of the angles is 360 deg.

    3x + 120 = 360

    Subtract 120 from both sides.

    3x = 240

    Divide both sides by 3.

    x = 80

    Answer: Each of the three congruent angles has measure 80 deg. The fourth angle has measure 120 deg.
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