Question 1078656


Two angles are {{{complementary}}} when they add up to {{{90}}} degrees.

let's angle be {{{alpha}}} and its complementary angle {{{beta}}}

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

given:
an angle measures {{{46}}}° {{{more}}} than the measure of a complementary angle

so, {{{alpha}}} measures {{{46}}}° {{{more}}} than {{{beta}}}=>

{{{alpha=beta+46}}}........eq.2

from eq.1 and eq.2 we have

{{{90-beta=beta+46}}}

{{{90-46=beta+beta}}}

{{{44=2beta}}}

{{{44/2=beta}}}

{{{highlight(beta=22)}}}° 

find {{{alpha}}}

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

{{{alpha=90-22}}}

{{{highlight(alpha=68)}}}°