Question 279791
<pre><font size = 4 color = "indigo"><b>
First let's learn what two supplementary angles are:

The straight angle indicated by the green arc is 180°.
The angle indicated by the blue arc is 123°, the given
angle.  The angle indicated by the red arc is the angle
we wish to find, I have labeled it x° 

{{{drawing(400,200,-1,1,0,1,line(-1,0,1,0),
line(0,0,cos(57*pi/180),sin(57*pi/180)),
blue(locate(-.27,.27,"123°")), green(arc(0,0,1,-1,0,180)),
red(locate(.15,.15,"x°")),
blue(arc(0,0,.5,-.5,57,180)),
red(arc(0,0,.3,-.3,0,57)),
green(locate(0,.6,"180°")) )}}}

So we see that 

{{{blue("123°") + red("x°") = green("180°")}}}

or

{{{red("x°") = green("180°")-blue("123°")}}}

{{{red("x°") = red("57°")}}}

Edwin</pre>