Q2 of 15 Page 137

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 angles?

Let the two angles be x and 2x

Increasing smaller by 6° and decreasing the larger by 6°, the ratio changes to 2: 3


⇒


⇒ 3×(x + 6) = 2×(2x – 6)


⇒ 3x + 18 = 4x – 12


⇒ 4x – 3x = 18 + 12


⇒ x = 30


Original angles are 30° and 2x = 2× 30 = 60°


∴ Original angles are 30° and 60°


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