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Question

Prove that sum of two complementary angles is 90.

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Solution

If two angles are complementary, that means that their sum is 90.
Two angles form a pair of complementary, supplementary and vertical angles. When the sum of two angles is 90, they are called complementary angles. Such a relationship may be useful in determining other unknown angles.


Complementary Angle Theorem
Statement: If two angles are each complementary to a 3rd angle, then they are congruent to each other. Or complements of the same angle are congruent.
Proof: Let A and B be complementary angles.
Step 1: B is a complement of A
Then A+B=90
(By complementary angles definition)
Step 2: Let A and C be complementary angles.
C is a complement of A
Then, A+C=90
From Step 1 and Step 2 we have,
A+B=A+C
B=C

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