Question

Two angles are in the ratio 1 : 2. On increasing the smaller angle by 6° and decreasing the larger angle by 6°, the ratio changed to 2 : 3. What were the original angle?

Answer 1

Let x be the smaller angle and 2x be the larger angle,

x + 6 : 2x – 6 = 2 : 3

2(2x – 6) = 3 (x + 6)

4x – 12 = 3x + 18

4x – 3x = 18 + 12 = 30; x = 30

Original smaller angle = x° = 30°

Original larger angle = 2x° = 60°