Question

The largest angle of triangle is twice the sum of the other two. The smallest is one-forth of the
largest. The smallest angle in degrees is:
a) 30°
by 60°
c) 45°
d) none of these​

Answer 1

Hi there here is your answer ,hope it helps you,

Let the other two angles be

{x}^{0} and \: {y}^{0}

The largest angel = 2(x + y)

since the sum of the angles of a triangle = 180°

∴ (x + y) + x + y = 180°

⇒2x + 2y + x +y = 180

⇒ 3x + 3y = 180

⇒x + y = 60

∴ Form (1), the largest angel = 2(60°) = 120°

It is given that the smallest angel = 1/4 (largest angel)

∴ y = 1 /4 × 120° =30°

Putting y = 30 in (2), x + 30.

hence the angles are 30°, 30°, 120°