Question 151591
We all know supplementary angles are {{{2}}} angles that add to 180 degrees.
For that reason, we can make an equation {{{A+B=180}}} ---------> eqn 1
It shows angle B is a supplemantary of angle A, and to satisfy the other condition 1 being {{{10percent}}} more than {{{4times}}} it's measure angle.
Putting that into eqn, {{{A=4B*1.10}}}, right? ------> eqn 2
We multiply by {{{1.10}}} because it's {{{10percent}}} more.
.
Substitute eqn 2 in eqn 1 we have
{{{(4B)(1.10)+B=180}}}
{{{4.40B+B=180}}}
{{{5.40B=180}}} ---------> {{{cross(5.40)B/cross(5.40)=cross(180)33.33333/cross(5.40)}}}
{{{B=33.333333deg}}} 
The other angle as per eqn 1: {{{A+33.333333=180}}} ----> {{{A=146.666667deg}}}
To check:
As it stated the supplement angle {{{10percent}}} more than {{{4times}}} it's measurement,go back eqn 2,
{{{146.666667=4(33.33333)*1.10}}}
{{{146.6666667=146.6666667}}}
Also, in eqn 1
{{{A+B=180}}} ------------> {{{146.666667+33.33333=180}}}
{{{180=180}}}
Thank you,
Jojo