Calculating With Supplements

In the diagrams below, the points A and B are located anywhere along the rays forming ∠C, whose measure is always 40°. The points A and B are connected by a line segment to form △ABC. The point D is the intersection of the bisectors of the exterior angles at A and B.

What is the measure of ∠ADB?

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Birthday Present (Dimes, Quarters)

Hartley and Bertha are pooling their money to buy their mother a birthday present. (Her birthday, by coincidence, turned out to be the day she was elected to the school board.) The two have $20.25 between them. Hartley has all of his money in dimes and Bertha’s is in quarters. Hartley has twice as many dimes as Bertha has quarters. How much money is Hartley contributing?

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Columbus to Cincinnati

At 12:00 noon, Lunis started driving from Columbus to Cincinnati at a steady 40 mph. Fifteen minutes later, at 12:15, Ethan started driving from Cincinnati to Columbus at a steady 50 mph. The two cars passed each other at a point midway between the two cities. Using this information, calculate the distance between Columbus and Cincinnati. (Is this distance correct?)

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