The angles of a triangle are in AP. The greatest angle is twice the least. Find all the angles of the triangle.


Let A, B and C be the three angles in AP (in degrees)


And A being the least and C being the greatest


Then


C = 2A [ Given][ eqn i]


B - A = C - B


2B = A + C


2B = A + 2A [ using eqn i]


2B = 3A


B = [ eqn ii]


Using the angle sum property of triangle


A + B + C = 180O


[ using i and ii]



9A = 360


A = 40O


[ using ii]


C = 2(40) = 80O [ using i]


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