duolingocom4

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To extend that further, if the polygon has x sides, the sum, S, of the degree measures of these x interior sides is given by the formula S = (x - 2)(180).

For example, a triangle has 3 angles which add up to 180 degrees. A square has 4 angles which add up to 360 degrees. For every additional side you add, you have to add another 180 degrees to the total sum.

Quadrilateral ABCD has, of course, four angles. Those four angles are in the ratio 2:3:3:4. Find the degree measure of the biggest angle of quadrilateral ABCD.

Steps:Add the terms 2x + 3x + 3x + 4xEquate the sum of the terms to 360Solve for xDetermine the angle measures in degrees.Solve

2x + 3x + 3x + 4x = 360 
12x = 360 
x = 360/12 
x = 30

Even though we know x = 30 we aren't done yet. We multiply 30 times 4 to find the biggest angle. Since 30 times 4 = 120, the biggest angle is 120 degrees. Likewise, the other angles are 3*30=90, 3*30=90, and 2*30 = 60.