Answer:
100°
Step-by-step explanation:
You have two supplementary angles in the ratio 7:2, and you want the measure of their positive difference.
Ratio units
The sum of supplementary angles is 180°. The sum of the ratio units in the ratio 7:2 is 7+2 = 9, so each ratio unit must stand for 180°/9 = 20°.
The difference in ratio units is 7 -2 = 5, so the difference in the angles will be 5·20° = 100°.
The measure of their difference is 100°.
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Additional comment
The two angles are 7·20° = 140°, and 2·20° = 40°. The difference is 140° -40° = 100°.
