Question

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

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

i.e.$\text{supplement of}a=36°$ …….from Step 1

Two angles are said to be supplementary if their sum is $180°$)

so, supplement of $a=180°-36°=144°$

Hence, the supplement of given angle is$144°$