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30 April, 03:51

Angle. How many sides does the polygon have?

27) In quadrilateral ABCD the measures of, ZA, ZB, 2C, and ZD are the ratio of 1:2:3-4,

respectively. Find the measures of the four angles.

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Answers (1)
  1. 30 April, 06:08
    0
    The measures of the four angles of quadrilateral ABCD are 36°, 72°, 108° and 144°

    Explanation:

    A polygon has three or more sides.

    Example:

    Triangle has 3 sides

    Square has 4 sides

    Pentagon has 5 sides and so on.

    27)

    In a quadrilateral ABCD, the measure of ZA, ZB, ZC and ZD are the ratio 1 : 2 : 3 : 4

    We know,

    sum of all the interior angles of a quadrilateral is 360°

    So,

    x + 2x + 3x + 4x = 360°

    10x = 360°

    x = 36°

    Thus, the measure of four angles would be:

    x = 36°

    2x = 2 X 36° = 72°

    3x = 3 X 36° = 108°

    4x = 4 X 36° = 144°

    Therefore, the measures of the four angles of quadrilateral ABCD are 36°, 72°, 108° and 144°
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