In a ABC, C = 3B = 2( A + B). Find the measure of each one of A, B and C.

We know that the sum of angles of a triangle is 180°


i.e. A + B + C = 180°


The given relation is C = 3B = 2(A + B) … (1)


3B = 2(A + B)


3B = 2A + 2B


2A = B


A = B/2


Substituting values in terms of B in equation (1),


B/2 + B + 3B = 180°


B/2 + 4B = 180°


B(9/2) = 180°


B = 180 × 9/2


B = 40°


Substituting B value in (1),


C = 3B = 3(40) = 120°


And A = B/2 = 40/2 = 20°


The measures are A = 20°, B = 40°, C = 120°.


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