Question

Find the angle which is four times its complement.

Answer 1

Hint: To solve this problem, we will assume the required angle to be x. Then, we will equate this to the required information given in this problem (that is, four times the complement of the angle). The complement of the angle x is given by (90 - x).

Complete step-by-step answer:
We need to find the angle which is four times its complement. Thus, we will first assume the angle to be x. Let, the complement of this angle be y. Now, by definition of the complement of angle, that is the sum of angles that add up to 90 degrees. Thus, we have,
x + y = 90
y = 90 – x -- (1)
Further, we know that the angle is four times the complement, thus, we have,
x = 4y
From eqn (1), we have,
$\Rightarrow$ x = 4(90-x)
$\Rightarrow$ x = 360 – 4x
$\Rightarrow$ 5x = 360
$\Rightarrow$ x = 72
Hence, the angle which is four times its complement is 72 degrees.

Note: In general, when we are asked to find the angle which is n times its complement (here, n can be any value like 1,2,3,4 and so on). We divide 90 into n+1 parts equally (in the above problem, since n was 4, we divide 90 into 4+1=5 parts). Thus, each part is equivalent to ${\displaystyle \frac{90}{5}}$ = 18. Now, we multiply any one part by n. Thus, in the above problem (for n=4), we have $18\times 4=72$. Thus, we get the same answer as the above solution.