Question 801205

Complementary angles add up to {{{90}}}°. 

let's an angle be {{{alpha}}} and its complement {{{beta}}}

given:

the measure of an angle whose measure is {{{1/2}}} of its complement angle


{{{alpha=(1/2)beta}}}....eq.1


{{{alpha+beta=90}}}.....eq.2....substitute {{{alpha}}} from eq.1

{{{(1/2)beta+beta=90}}}....solve for {{{beta}}}

{{{3beta/2=90}}}

{{{3beta=180}}}

{{{beta=180/3}}}

{{{beta=60}}} => {{{alpha=(1/2)beta=60/2=30}}}

so, the measure of an angle whose measure is {{{1/2}}} of its complement angle
 is {{{alpha =30}}}