Question 94082
Question:

Two angles are supplementary. One angle measures 12degrees more than the other. Find the measures of the angles.


Answer:

If the two angles add to 180°, we say they "Supplement" each other. 


Assume that one angle = X degrees.


The other angle = X + 12 degrees ( it is given that other angle is 12 degrees more than the first one)


Since supplementary angles add to 180 degrees, we can write,


X + ( X + 12 ) = 180



==> X + X + 12 = 180


==> 2X + 12 = 180



Subtract 12 from both sides 


==> 2X + 12 - 12 = 180 - 12



==> 2X   = 168 



Divide both sides by 2



==> {{{ 2X/2 = 168/2}}}



==>  X = 84



That is one angle is 84 degrees


So the other angle is X +12 = 84 + 12 = 96 degrees.


So the supplementary angles are, {{{ 84 }}} and {{{96}}}



Hope you found the explanation useful.


Regards.


Praseena.