An angle is 10° more than the measure of its complement. Find the number of degrees in each angle. The angles measure degrees.

Question

Prego

Mathematics

17 December, 00:21

An angle is 10° more than the measure of its complement. Find the number of degrees in each angle. The angles measure degrees.

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Answers (1)

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Ramon Rush · Answer 1

Let the angle be x. The complement of this angle would then be 90-x.

We are told that x is 10 more than 90-x, or x is 90-x+10, or x = 100 - x.

If x = 100 - x, then 2x = 100, and x = 50.

Check: If one angle is 50 degrees, the complement is 90-50, or 40 degrees.

Are 50 and 40 complementary? Yes. They add up to 90. Is 50 10 more than 40? Yes.

The measurements of these two angles are 40 and 50 degrees.