Question

Find the angle which is four times its complement.

Answer 1

Hint: Two angles are complementary, if they sum up to 90$^{\circ}$, i.e. if we have one angle $\angle{A}$ and the other angle is $\angle{B}$, then $\angle{A}$ and $\angle{B}$ are supplementary, if $\angle A+\angle B={{90}^{{}^\circ }}$. In terms of geometry, two angles which are complements of each other form a right angle. Also, if two angles are complementary, we say the first angle is “complement” of the other, i.e. in this case $\angle{A}$ is a “complement” of $\angle{B}$. Here, we will take the angle to be $x$, and we will try to create an equation and solve that to find the angle.

Complete step by step answer:
We need to find an angle that is four times its complement. Let that angle be $x$. The complement of an angle means we just need to subtract that angle from 90. So the complement of $x$ is $90-x$. So, according to the question:
$x=4\times\left(90-x\right)$
We first open the brackets, we get:
$x=360-4x$
Take $-4x$ to the other side of the equation, we get:
$x+4x=360$
Summing $x$ and 4$x$ gives 5$x$, so we get:
$5x=360$
$\implies x=72^{\circ}$
Hence, we have found the angle which is 4 times its complement.

Note: When we calculate the complementary angle, do not confuse it with supplementary angle and subtract it from ${{180}^{{}^\circ }}$. It is a common mistake, so always read the statement of what has been asked and then do what needs to be done. Take care of calculation mistakes while subtracting. Do NOT subtract the angle ${{90}^{{}^\circ }}$ from the angle. You need to subtract the given angle from ${{90}^{{}^\circ }}$.