The measures of the three angles of a triangle are in the ratio 17 : 13 : 15. Find the positive difference between the greatest and the smallest of these three angles.

Question

Accepted Answer

Let the measures of the three angles be 17x, 13x, and 15x. The sum of the angles in a triangle is 180°.

So, 17x + 13x + 15x = 180°
=> 45x = 180°
=> x = 4°

Therefore, the angles are:
17x = 17 × 4 = 68°
13x = 13 × 4 = 52°
15x = 15 × 4 = 60°

The greatest angle is 68°, the smallest is 52°.
The positive difference = 68° - 52° = 16°.

However, let's double-check the calculation:
17 + 13 + 15 = 45
x = 180/45 = 4
Angles: 68°, 52°, 60°
Difference: 68° - 52° = 16°

So the correct answer is 16°, which matches option 1. The answer key provided in the question seems to have a mismatch. The correct answer is 16°.

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