Question 120571
I think you meant to say 'supplemental' angles.


Supplemental angles are angles whose measures sum to either 180 degrees or {{{pi}}}, depending on the measurement system you are using.  Let's use 180 degrees for this example.


If the measure of one of the angles is x degrees, then the measure of the other angle must be 180 - x degrees.  And we know that these two angles are in the ratio of 7:5.  So we can write:


{{{(180-x)/x=7/5}}}


Since we have created a proportion, we can cross multiply and solve:


{{{5(180-x)=7x}}}


{{{900-5x=7x}}}


{{{900=12x}}}


{{{x=75}}}.


So 75 degrees is the measure of one of the angles, and the other angle must then be 180 - 75 = 105.


Check the answer:

Reduce the fraction {{{105/75}}} to lowest terms.


{{{105/75=(15*7)/(15*5)=7/5}}}, answer checks.