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The difference of two complementary angles is 27 degrees. Find the measures of the angles (in degrees).

User Ikwillem
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1 Answer

4 votes

Answer:

58.5° and 31.5°

Explanation:

Complementary angles are two angles whose sum is 90 degrees. Let x be one of the complementary angles, then the other complementary angle can be represented as 90 - x.

The problem tells us that the difference between the two complementary angles is 27 degrees, so we can set up the following equation:

x - (90 - x) = 27

Simplifying and solving for x, we get:

x - 90 + x = 27

2x - 90 = 27

2x = 117

x = 58.5

So one of the complementary angles is 58.5 degrees, and the other complementary angle can be found by subtracting this value from 90:

90 - 58.5 = 31.5

Therefore, the measures of the angles are [58.5° and 31.5°.]

User Pouryak
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