Question 60

The ratio of the angles of a triangle is 1:2/3:3 then the smallest angle is

Solution

Let the angles of triangle be $$x, \frac{2x}{3}$$ and $$3x$$

Multiplying by 3, => Angles = $$3x,2x,9x$$

Sum of angles = $$180^\circ$$

=> $$3x+2x+9x=180^\circ$$

=> $$14x=180^\circ$$

=> $$x=\frac{180}{14}=\frac{90}{7}$$

$$\therefore$$ Smallest angle = $$2x$$

= $$2 \times \frac{90}{7}=\frac{180}{7}$$

= $$25\frac{5}{7}^\circ$$

=> Ans - (A)

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