If angles A, B, C and D of the quadrilateral ABCD, taken in order, are in the ratio 3:7:6:4, then ABCD is
Question
If angles A, B, C and D of the quadrilateral ABCD, taken in order, are in the ratio 3:7:6:4, then ABCD is
Solution
To solve this problem, we need to use the fact that the sum of the angles in a quadrilateral is always 360 degrees.
Let's assign variables to the angles: A = 3x, B = 7x, C = 6x, and D = 4x.
According to the given ratio, the sum of these angles is 3x + 7x + 6x + 4x = 20x.
Since the sum of the angles in a quadrilateral is 360 degrees, we can set up the equation 20x = 360.
To solve for x, we divide both sides of the equation by 20: x = 360/20 = 18.
Now that we know the value of x, we can find the measures of the angles: A = 3x = 3(18) = 54 degrees, B = 7x = 7(18) = 126 degrees, C = 6x = 6(18) = 108 degrees, and D = 4x = 4(18) = 72 degrees.
Therefore, the measures of the angles of the quadrilateral ABCD are 54 degrees, 126 degrees, 108 degrees, and 72 degrees.
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