Question 1157256


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

let an angle be {{{alpha}}}

its complement is {{{90-alpha}}}

and its supplement is {{{180-alpha}}}

when you add the measure of an angle to twice the measure of its complement, we have

{{{alpha+2(90-alpha)}}}

 the sum is the measure of the angles supplement, {{{180-alpha}}}


set up equation and prove it is true statement:


{{{alpha+2(90-alpha)=180-alpha}}}......solve for {{{alpha}}}

{{{alpha+180-2alpha=180-alpha}}}

{{{2alpha+180-2alpha-180=0}}}

{{{0=0}}}=> true


an examples to show that, when you add the measure of an angle to twice the measure of its complement, the sum is the measure of the angle's supplement:


 let's say that the angle  {{{alpha=30}}} degrees  

so, we have

{{{alpha+2(90-alpha)=180-alpha}}}

{{{30+2(90-30)=180-30}}}

{{{30 + 120 = 150}}}

{{{150 = 150}}}


same will be if {{{alpha=60}}} degrees, {{{alpha=45}}} degrees, {{{alpha=1}}} degrees,....