sum of two complementary angles is 90 degrees. justify answer
Answers
Answer:
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
flag
when we add 2 angles and we get sum as 90 then we can say sum of two complementary angles is 90 degrees !