The angles of a quadrilateral 24,3x,120,and 144 find x
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Answer:
First, we’ll find the number of degrees in the quadrilateral. The formula for the number of degrees in an n-sided polygon is (n−2)⋅ 180˚ . Plugging in 4 (because a quadrilateral has 4 sides), we get (4−2)⋅180˚=360˚ . Therefore, there are 360 degrees in the quadrilateral.
Next, the angle is directly proportional to the opposite side, meaning that the side with the largest side will have the largest opposite angle. The largest side is 6 , so that will correspond to the largest angle.
The amount of the “budget” of the quadrilateral the particular angle will get has the same proportions as the length of the opposite does to the total perimeter, so first we’ll find the ratio of the length of the side opposite the total perimeter.
The total perimeter is 2+3+4+6=15 , so the ratio of the largest angle to the total sum of the angles in the quadrilateral will be 615=25 . Therefore, we now have the equation: A360˚=25 . Solving this for A , we see that A=2⋅360˚5=144˚ .
Therefore, the largest angle in the quadrilateral is 144
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