Question

An angle is equal to one-fifth its complement.
Find the angle's measure

Answer 1

Answer :-

`\longrightarrow \sf The \: angle's \:measure \:is \:15⁰`

Solution:-

Two angles are said to be complimentary if their sum is 90⁰. These angles are called compliment of each other.

Assumption :-

`\red{\leadsto}\:`
`\textsf{let \: the \: angle \: be \:x }`

`\green{\leadsto}\:`
`\textsf{Complimentary \:angle \:will \:be \:5x }`
`\sf`

`\green{ \underline { \boxed{ \sf{Sum \: of \: complimentary \:angles = 90⁰}}}}`

`\begin{gathered}\\\implies\quad \sf x+5x = 90⁰ \\\end{gathered}`

`\begin{gathered}\\\implies\quad \sf 6x = 90⁰ \\\end{gathered}`

`\begin{gathered}\\\implies\quad \sf x = (90)/(6) \\\end{gathered}`

`\begin{gathered}\\\implies\quad \sf x = 15⁰\\\end{gathered}`