Question

How many degrees are there in an angle which is one-fifth of its complement?

Answer 1

Hint: In order to solve this question, we need to understand what the question is. The question is asking us to find the angle which is one – fifth of complement and a complementary angle is the angle which is when added to the angle given us the sum of \[{{90}^{o}}\].

Complete step-by-step answer:
In this question, we are asked to find the value of an angle which is one – fifth of its complementary. Let us consider the angle as x. So, we can say that the complementary angle of x is (90 – x), because complementary angles are those which give us the sum of \[{{90}^{o}}\].
Now, we have been given a condition that its angle is one-fifth of its complement. Mathematically, we can write it as
\[x=\dfrac{1}{5}\left( 90-x \right)\]
Now, we will cross multiply the equation. So, we will get,
\[5x=90-x\]
Now, we will take all the terms with the variable to the left-hand side. So, we will get,
\[5x+x=90\]
\[6x=90\]
Now, we will divide the equation by 6, so we will get,
\[\dfrac{6x}{6}=\dfrac{90}{6}\]
\[x=15\]
Therefore, we can say that there are 15 degrees in an angle which is one-fifth of complement.

Note: In this question, the possible mistake one can make is by equating x with one – fifth of \[{{90}^{o}}\], which is definitely wrong and will give us the wrong answer. So, read the question twice before answering it.