Question

Find the complements of the following angles:-
\[
  {\text{a) }}{45^0} \\
  {\text{b) }}{8^0} \\
  {\text{c) }}{20^0} \\
  {\text{d) }}{25^0} \\
  {\text{e) }}{78^0} \\
  {\text{f) }}{45^0} \\
 \]

Answer 1

Hint: - Here we go through by finding the complements of each angle one by one as we know the complement of angle x is ${90^0} - x$. By applying this we will get the answer.

Complete step-by-step answer:
Here in the question we have to find complementary angles.
As we know when the sum of two angles is 90°, then the angles are known as complementary angles. In other words, if two angles add up to form a right angle, then these angles are referred to as complementary angles. Here we say that the two angles complement each other. Suppose if one angle is x then the other angle will ${90^0} - x$.
Now by applying the definition we will get our answer.
a) Complimentary of ${45^0} = {90^0} - {45^0} = {45^0}$
b) Complimentary of ${8^0} = {90^0} - {8^0} = {82^0}$
c) Complimentary of ${20^0} = {90^0} - {20^0} = {70^0}$
d) Complimentary of ${25^0} = {90^0} - {25^0} = {65^0}$
e) Complimentary of ${78^0} = {90^0} - {78^0} = {12^0}$
f) Complimentary of ${45^0} = {90^0} - {45^0} = {45^0}$

Note: - Whenever we face such a type of question we have to go through the definition of the complementary angles and then find out the answer. But we generally confuse in complementary and supplementary angles and make mistakes in answers. Always keep in mind complimentary means sum of two angles is ${90^0}$ and supplementary means sum is ${180^0}$