SOLUTION: The four angles of a quadrilateral form an arithmetic sequence. The largest is 15 degrees less than twice the smallest. What is the degree measure of the largest angle?

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Question 1122231: The four angles of a quadrilateral form an arithmetic sequence. The largest is 15 degrees less than twice the smallest. What is the degree measure of the largest angle?
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39749) About Me  (Show Source):
Answer by ikleyn(53646) About Me  (Show Source):
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Let the smallest angle is x degrees and the largest is y degrees.


The sum of all four interior angles of a quadrilateral is 360 degrees.


Since four angles form arithmetic progression, the formula for their sum is


    %28%28x+%2B+y%29%2F2%29%2A4 = 360,   which implies


    x + y = 180.      (1)


The second equation is


     y = 2x + 15.     (2)


Substitute eq(2) into eq(1). You will   get


     x + (2x+15) = 180,

     3x = 180 - 15 = 165  ====>  x = 165%2F3 = 55.


Answer.  The smallest angle is 55 degrees.   The greatest angle is  2x + 15 = 2*55 + 15 = 110 + 15 = 125 degrees.

Solved.