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 angles ?​

Answer 1

Step-by-step explanation:

Given :-

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.

To find :-

What were the original angles ?

Solution :-

Given that :

The ratio of two angles = 1 : 2

Let they be X° and 2X°

On increasing the smaller angle by 6

Then it becomes = (X°+6)

On decreasing the larger angle by 6

Then it becomes = (2X°-6)

Their ratio = (X+6)° : (2X-6)°

Given that

On increasing the smaller angle by 6 and decreasing the larger angle by 6, the ratio changed to 2:3.

=> (X+6)° : (2X-6)° = 2 : 3

=> (X+6)° / (2X-6)° = 2 / 3

On applying cross multiplication then

=> 2(2X-6)° = 3(X+6)°

=> 2(2X°)-(2×6°) = 3X°+3×6°

=> 4X° -12° = 3X° +18°

=> 4X° - 3X° = 18° + 12°

=> X° = 30°

The value of X = 30°

Now ,2X° = 2(30°) = 60°

The angles = 30° and 60°

Answer:-

The original angles for the given problem are 30° and 60°

Check:-

The angles = 30° and 60°

Their ratio = 30:60=1:2

On increasing the smaller angle by 6 and decreasing the larger angle by 6, the ratio changed to 2:3.

=> (30°+6°) : (60°-6°)

=> 36° : 54°

=> 2 : 3

Verified the given relations in the given problem.

Used formulae :-

• a : b can be written as a/b