Question 9

# A triangle has two of its angles in the ratio of 1 : 2. If the measure of one of its angles is 30 degrees, what is the measure of the largest angle of the triangle in degrees ?

Solution

Case 1 : Let the first angle be 30°

So according to the ratio of 1 : 2, the other angle = 60°

=> Third angle = $$180^{\circ} - (30^{\circ} + 60^{\circ}) = 180^{\circ} - 90^{\circ} = 90^{\circ}$$

Case 2 : Let the third angle be 30°

=> First and second angles respectively are = $$x , 2x$$

=> $$x + 2x + 30^{\circ} = 180^{\circ}$$

=> $$3x = 180^{\circ} - 30^{\circ} = 150^{\circ}$$

=> $$x = \frac{150^{\circ}}{3} = 50^{\circ}$$

Thus, largest angle = $$2 \times 50^{\circ} = 100^{\circ}$$

$$\therefore$$ Largest angle can be either 90 or 100°

=> Ans - (D)