Of the three angles of a triangle, one is half of the greatest and thrice the smallest then find the angles

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Solution

$\begin{matrix} L e t t h e a n g l e b e x g r e a t e s t a n g l e = 2 x s m a l l e s t a n g l e = \frac{x}{3} N o w x + 2 x + \frac{x}{3} = 180 \Rightarrow 10 x = 180 \times 3 \Rightarrow 10 x = 540 ∴ x = 54 T h e n g r e a t e s t a n g l e = 2 \times 54 = 108 s m a l l e s t a n g l e = \frac{54}{3} = 18 \end{matrix}$

Hence, this is the answer.

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