Question 646747
Two angles are complementary if they add up to {{{90}}} degrees.

let's angles be {{{alpha}}} and {{{beta}}}

so, 
given:{{{alpha+beta=90}}}.........1

One angle (let it be {{{alpha}}})  is {{{nine}}}{{{ times}}} its complement {{{beta}}} increased by {{{50}}} degrees ; so, we have:

{{{alpha=9*beta+50}}}........2

go to {{{alpha+beta=90}}}.........1...replace {{{alpha}}} from 1 and solve for {{{beta}}}

{{{9*beta+50+beta=90}}}

{{{9*beta+beta=90-50}}}

{{{10*beta=40}}}

{{{highlight(beta=4)}}}

now find {{{alpha}}}

{{{alpha=9*beta+50}}}........2

{{{alpha=9*4+50}}}

{{{alpha=36+50}}}

{{{highlight(alpha=86)}}}