Question

The complement of \[\left( {{{90}^ \circ } - a} \right)\] is-
A. –a
B. $\left( {{{90}^ \circ } + a} \right)$
C. $\left( {{{90}^ \circ } - a} \right)$
D. a

Answer 1

Hint: Here\[\left( {{{90}^ \circ } - a} \right)\] is measure of an angle. Complementary angles are angles such that when they are added their sum is equal to right angle $\left( {{{90}^ \circ }} \right)$ . So assume the complement angle to be x and equate the sum of the angles to right angle.

Complete step by step Answer:

There are five types of angles one of which are complementary angles. Two angles are complementary only if when they are added their sum is equal to ${90^ \circ }$.
Here the given angle is \[\left( {{{90}^ \circ } - a} \right)\] and we have to find its complementary angle.
Let us assume the complement angle to be x then from the definition of complementary angles we know that their sum should be equal to ${90^ \circ }$. Then,
$ \Rightarrow x + \left( {{{90}^ \circ } - a} \right) = {90^ \circ }$
On opening the bracket we get,
$ \Rightarrow x + {90^ \circ } - a = {90^ \circ }$
On simplifying we get,
$ \Rightarrow x - a = {90^ \circ } - {90^ \circ }$
$ \Rightarrow x - a = 0$
On transferring ‘a’ from left to right its sign changes and we get,
$ \Rightarrow x = a$
Hence, the complement angle is ‘a’
Answer- The correct answer is D.

Note: Remember that Complementary angles are angles such that when they are added their sum is equal to right angle $\left( {{{90}^ \circ }} \right)$
The other types of angles are as follows-
1) Acute angle- It is an angle which measures less than ${90^ \circ }$
2) Obtuse angle-It is the opposite of an acute angle. It measures greater than ${90^ \circ }$ but less than ${180^ \circ }$.
3) Reflex angle-It is an angle that measures more than ${180^ \circ }$ but less than ${360^ \circ }$.
4) Supplementary angles-Two angles are said to be supplementary angles if their sum is equal to ${180^ \circ }$