Question 1152103

complementary angles are two angles whose sum is {{{90}}} degrees

let the larger angle be {{{alpha}}} and the smaller angle {{{beta}}}

{{{alpha+beta=90}}}.......eq.1

if the measure of the larger angle is {{{10}}} more than {{{4}}} times the measure of the smaller angle, we have

{{{alpha=4*beta+10}}}........eq.2-> substitute in eq.1

{{{4*beta+10+beta=90}}}.......eq.1

{{{5*beta=90-10}}}

{{{5*beta=80}}}

{{{beta=80/5}}}

{{{beta=16}}} degrees

then

{{{alpha+beta=90}}}.......eq.1

{{{alpha+16=90}}}

{{{alpha=90-16}}}

{{{alpha=74}}}