Question

write an equation and solvefour times the complement of an angle is 40° lessthan twice the angles supplement. Find the angle,its complement, and its supplement

Answer 1

Let the angle be 'x' degrees.

The complement (C) of the corresponding angle will be,

`C=90-x`

And the supplement (S) of the corresponding angle will be,

`S=180-x`

According to the condition given in the problem,

`4C=2S-40^{}`

Substitute the values,

`\begin{gathered} 4(90-x)=2(180-x)-40 \\ 360-4x=360-2x-40 \\ -4x=-2x-40 \\ 4x-2x=40 \end{gathered}`

Simplify the expression further,

`\begin{gathered} 2x=40 \\ x=(40)/(2) \\ x=20 \end{gathered}`

Substitute this value of 'x' to obtain the complement and supplement angles as follows,

`\begin{gathered} C=90-20=70 \\ S=180-20=160 \end{gathered}`

Thus, the angle measures 20 degrees, its complement measures 70 degrees, while its supplement measures 160 degrees.