Question

An angle is$\frac{1}{5}$times of a straight angle. Find the complement of this angle.

Answer 1

Step 1: Finding $\frac{1}{5}$times of a straight angle.

An angle whose measure is exactly $180°$is called a straight angle.

let the requires angle be $a$.

so, according to question

$$\begin{gathered} \Rightarrow a=\frac{1}{5}ofstraightangle \\ \Rightarrow a=\frac{1}{5}of180° \\ \Rightarrow a=\frac{1}{5}\times 180° \\ \Rightarrow a=36° \end{gathered}$$

Step 2: Finding complement of given angle

the given angle is $a=$$\frac{1}{5}$times of a straight angle.

i.e.$complementofa=36°$ …….from Step 1

Two angles are said to be complementary if their sum is $90°$)

so, complement of $a=90°-36°=54°$

Hence, complement of given angle is $54°$