SOLUTION: If the angles of a six sided polygon are in the ratio 2:3:4:5:6:7 what is the degree measure of the largest angle? 140/3 280/3 140 560/3

Algebra ->  Numeric Fractions Calculators, Lesson and Practice -> SOLUTION: If the angles of a six sided polygon are in the ratio 2:3:4:5:6:7 what is the degree measure of the largest angle? 140/3 280/3 140 560/3      Log On


   

Question 1119306: If the angles of a six sided polygon are in the ratio 2:3:4:5:6:7 what is the degree measure of the largest angle?
140/3
280/3
140
560/3
Answer by ikleyn(52771) About Me  (Show Source):
You can put this solution on YOUR website!
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The six angles measures are 2x, 3x, 4x, 5x, 6x and 7x,  where x is their common measure.


The sum of interior angles of any n-sided polygon is  (n-2)*180 degrees, therefore


    2x + 3x + 4x + 5x + 6x + 7x = 4*180,    or

    27x = 720

    x = 720%2F27 = 262%2F3 degrees.


The greatest angle measure is  7 times 262%2F3 degrees,  or 1862%2F3 degrees = 560%2F3 degrees.

Solved.