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.

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Step 1: Let the three angles be 17x, 13x, and 15x.
Step 2: Since the sum of angles in a triangle is 180°, we have:
17x + 13x + 15x = 180
45x = 180
x = 180 / 45 = 4
Step 3: Calculate each angle:
Greatest angle = 17x = 17 * 4 = 68°
Smallest angle = 13x = 13 * 4 = 52°
Step 4: Find the positive difference:
68° - 52° = 16°
Therefore, the positive difference between the greatest and smallest angles is 16°.

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