1. 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 ?
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By: anil on 05 May 2019 01.35 am
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 = $$2 imes 50^{circ} = 100^{circ}$$ $$ herefore$$ Largest angle can be either 90 or 100° => Ans - (D)
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