Question 949556

 

Find the measure of an angle such that the difference between the measures of its supplement and three times its compliment is 10 degrees.

Two Angles are Supplementary if they add up to {{{180}}} degrees.
Two Angles are Complementary if they add up to {{{90}}} degrees.

if one angle is {{{alpha}}} then its supplement   is {{{180-alpha}}} and its complement is {{{90-alpha}}}


you are given:

an angle such that the difference:

 between the measures of its supplement {{{180-alpha}}}
and {{{3}}} times its compliment {{{90-alpha}}}: {{{3(90-alpha)}}}
is : equal {{{10}}} degrees 

{{{(180-alpha)-3(90-alpha)=10}}} ...........solve for {{{alpha}}}

{{{180-alpha-270+3alpha=10}}}

{{{-90+2alpha=10}}}

{{{2alpha=10+90}}}

{{{2alpha=100}}}

{{{highlight(alpha=50)}}}-> your angle

find its supplement and complement 
 its supplement {{{180-alpha=180-50=highlight(130)}}}
its compliment {{{90-alpha=90-50=highlight(40)}}}

check is the difference of {{{130}}} and {{{3*40}}} is equal {{{10}}}

{{{130-3*40=10}}}
{{{130-120=10}}}
{{{10=10}}}...true