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°.