Question

Find the measure of an angle which is $36{}^\circ $ more than its complement.

Answer 1

Hint: Let the angle that we are asked to find be $x$ and its complement be y. We know that two angles are said to be complement of each other if and only if there sum is equal to $90{}^\circ $ . So, represent this mathematically to get one equation in x and y. The other equation can be formed by using the fact that the angle x is $36{}^\circ $ more than its complement y. Solve the two equations to get the value of x.

Complete step-by-step answer:
Let us start the solution to the above question by letting the angle that we are asked to find be $x$ and its complement be y.

Now we know that two angles are said to be complement of each other if and only if their sum is equal to $90{}^\circ $ . So, if we represent this in form of equation, we get
$x+y=90{}^\circ ........(i)$
Also, it is given that the measure of an angle which is $36{}^\circ $ more than its complement, i.e., x is $36{}^\circ $ more than y. If we represent this mathematically, we get
$x-y=36{}^\circ ..........(ii)$
Now we will add equation (i) and equation (ii). On doing so, we get
$x+y+x-y=90{}^\circ +36{}^\circ $
$\Rightarrow 2x=126{}^\circ $
$\Rightarrow x=63{}^\circ $
Hence, we can conclude that the answer to the above question is $63{}^\circ $ .

Note:Be careful about what is given in the question, whether the complement is greater or the angle is greater than its complement. It is also important that you know that if the sum of two angles is $90{}^\circ $ or ${{\dfrac{\pi }{2}}^{c}}$ then they are said to be complement of each other.