Question

a) Three angles on a straight line at a point are in the ratio 3 : 2:5. Find the difference between the largest and the smallest angle.​

Answer 1

Answer:

  54°

Step-by-step explanation:

The ratio values can be used to find the angles, then the desired difference can be found. Alternatively, the desired difference can be figured in terms of the ratio units given.

Ratio of difference to whole

The number of ratio units representing the largest angle is 5. The number of ratio units representing the smallest angle is 2. The difference of these is 5 -2 = 3.

The total number of ratio units is 3 +2 +5 = 10. This is the number of ratio units representing the straight angle, 180°.

The difference is 3 of those 10 ratio units:

  3/10 × 180° = 54° . . . . . . largest - smallest difference

Find the angles

There are 10 ratio units in total (3+2+5=10), so each represents 180°/10 = 18°. Multiplying the given ratios by 18° gives the angle values:

  3×18° : 2×18° : 5×18° = 54° : 36° : 90°

The difference between the largest and smallest is ...

  90° -36° = 54° . . . . . . largest - smallest difference