SOLUTION: Prove that the sum of the measures of the complements of complementary angles is 90 degrees.
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Question 443605: Prove that the sum of the measures of the complements of complementary angles is 90 degrees.
Answer by swincher4391(1107) (Show Source): You can put this solution on YOUR website!
Let A and B be two complementary angles. We need to show that the complements of these two angles have a sum of 90. Since A and B are complementary. Then A + B = 90. Let C be the complement of A. Then A + C = 90. Let D be the complement of B. Then B + D = 90. So show that C + D = 90.
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A + C = 90 and B + D =90
So A = 90 - C and B = 90 - D
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Since A + B = 90
Then 90 - C + 90 - D = 90
180 - C - D = 90
90 = C + D
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Which is what we wanted to show.
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Then C (the complement of A) and D(the complement of B) are complements of each other.
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