Question

Find the angle which is 6 times its complement​

Answer 1

$\qquad\qquad\huge\underline{{\sf Answer}}$

$\textsf{Let the angle be x, then it's complement }$$\textsf{will be }$ ~

$\qquad \sf \dashrightarrow \: \dfrac{x}{6}$

$\textsf{And as we know, sum of complimentary angles }$ $\textsf{measure 90°}$

$\qquad \sf \dashrightarrow \: x + \dfrac{x}{6} = 90$

$\qquad \sf \dashrightarrow \: \dfrac{6x + x}{6} = 90$

$\qquad \sf \dashrightarrow \: 7x = 90 \times 6$

$\qquad \sf \dashrightarrow \: x = \dfrac{540}{7}$

$\textsf{So, the required angle is }$ ${\sf{{\dfrac{540\degree}{7}}}}$

Answer 2

Using subUsing substitution for Y, the top equation becomes X +6z= 180. Using elimination with X +6z= 180 and subtracting X+z= 90 result is 5z=90 and Z= 18. So complimentary angle is 18°