In a Find the three angles.


Given that,

C = 3 B = 2( A + B) 3 B = 2( A + B)


3 B = 2 A + 2 B


B = 2 A


2 A - B = 0 … (i)


We know that the sum of the measures of all angles of a triangle is 180°. Therefore,


A + B + C = 180°


A + B + 3 B = 180°


A + 4 B = 180° … (ii)


Multiplying equation (i) by 4, we obtain 8 A - 4 B = 0 … (iii)


Adding equations (ii) and (iii), we obtain 9 A = 180°


A = 20°


From equation (ii), we obtain 20° + 4 B = 180°


4 B = 160°


B = 40°


C = 3 B


= 3 x 40° = 120°


Therefore, A, B, C are 20°, 40°, and 120° respectively.


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