Question

Two complementary angles differ by ${\text{1}}{{\text{2}}^0}$, find the angles?

Answer 1

Hint: In the question , the first thing that we should do is to write the definition of complementary angles. Complementary angles are the two angles whose sum is ${\text{9}}{{\text{0}}^0}$. After this assume one of the angle as A then other becomes \[{\text{(9}}{{\text{0}}^0}{\text{ - A)}}\] and then use the given information in question to form the equation.

Complete step-by-step answer:

In the question, we have two complementary angles whose difference is given.

First of all we will see the definition of complementary angles.

Complementary angles are the two angles whose sum is ${\text{9}}{{\text{0}}^0}$.

Now, let the first complementary angles be A and \[{\text{(9}}{{\text{0}}^0}{\text{ - A)}}\]

According to question-
Two complementary angles differ by ${\text{1}}{{\text{2}}^0}$

So,
$ \Rightarrow $\[{\text{(9}}{{\text{0}}^0}{\text{ - A)}}\]- ${\text{A}}$= ${\text{1}}{{\text{2}}^0}$
$ \Rightarrow $ ${\text{9}}{{\text{0}}^0}$- ${\text{2A}}$= ${\text{1}}{{\text{2}}^0}$
$ \Rightarrow $ ${\text{2A}}$= ${\text{7}}{{\text{8}}^0}$
$ \Rightarrow $ ${\text{A = 3}}{{\text{9}}^0}$
$\therefore $ First angle = ${\text{A}}$=${\text{3}}{{\text{9}}^0}$
And second angle (complementary angle) = \[{\text{(9}}{{\text{0}}^0}{\text{ - A)}}\]
                                                                    =${\text{(9}}{{\text{0}}^0}{\text{ - 3}}{{\text{9}}^0}{\text{)}}$
                                                                    = ${\text{5}}{{\text{1}}^0}$

Therefore,
 ${\text{3}}{{\text{9}}^0}$ and ${\text{5}}{{\text{1}}^0}$ are two complementary angles.

Note: In this type of question, you should remember the definition of complementary angles.In place of complementary angles, if supplementary angle is given then we consider two supplementary angles be A and \[{\text{(18}}{{\text{0}}^{\text{o}}}{\text{ - A)}}\].Because Supplementary angles are the two angles whose sum is ${180^{\text{o}}}$.