How to Determine the Angles in a Quadrilateral Knowing the Length of the Sides

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Determining the angles in a quadrilateral depends greatly on which kind of quadrilateral it is. Determine the angles in a quadrilateral with help from an experienced mathematics professional in this free video clip.

Part of the Video Series: Math Calculations
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Hi, I'm Drew Moyer, and this is how to determine the angles in a quadrilateral when given the sides. Determining the angles in a quadrilateral depends greatly on which kind of quadrilateral it is. Suppose I'm given this trapezoid. Now because I know that angle C is a right angle, I know that angle B must also be a right angle because I have two sets of parallel lines and these two angles must be supplementary. To find these two, it's going to be a little more tricky and I can get them by dropping this altitude down just like this, making a right angle there and instead of a trapezoid now I have a rectangle and a right triangle which is going to be a huge asset for me in discovering these next two angles, A and D. Now if I know that this side is 5 and since I made a rectangle over here I know that this altitude must be 4, I can use a trigonometric function to find angle D and I have the side opposite to angle D and the hypotenuse so I know that I'm going to be using sin. So I would do sin of angle D equals opposite 4/hypotenuse 5 which is equal to .8 and now I would turn right back around and plug this .8 into an inverse sin function in order to get what angle D actually equals. So sin inverse of .8 is equal to approximately 53.13 degrees. So now I've just found angle D and again, because it's a trapezoid and I know that the top and bottom must be parallel lines, I know that angle A must be supplementary to angle D which I can find by doing 180 minus 53.13 and it equals 127.87 degrees. And now I have all the angles in the trapezoid solved for. So, I'm Drew Moyer, and this was how to determine the angles in a quadrilateral when given the sides.

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