Respuesta :
Let us translate the statements in the problem to mathematics equations
Let the angle is x degree
So its supplement is
[tex]180^{\circ}-x[/tex]And its complement is
[tex]90^{\circ}-x[/tex]Since the supplement is 6 times its complement, so Multiply the complement by 6 and equate the answer by the supplement
[tex]180-x=6(90-x)[/tex]Let us simplify the right side
[tex]180\text{ - x = 6(90) - 6(x)}[/tex][tex]180\text{ - x = 540 - 6x}[/tex]Now let us solve the equation to find x
At first, add 6x to both sides to put x in the left side
[tex]\begin{gathered} 180\text{ - x + 6x = 540 - 6x + 6x} \\ 180\text{ + 5x = 540} \end{gathered}[/tex]Now subtract 180 from both sides to put the number in the right side
[tex]\begin{gathered} 180\text{ - 180 + 5x = 540 - 180} \\ 5x\text{ = 360} \end{gathered}[/tex]Divide both sides by 5 to get x
[tex]\begin{gathered} \frac{5x}{5}=\frac{360}{5} \\ x=72^{\circ} \end{gathered}[/tex]So the measure of the angle is 72 degrees
You can check the answer
180 - 72 = 108
90 - 72 = 18
18 * 6 = 108
So the supplement of 72 is six times its complement
