# Exterior angle

Exterior angles can be calculated with the knowledge that angles on a line add up to 180 degrees.

Since we know that angles in a triangle add up to 180 degrees, we can calculate x as:

$40\textdegree+56\textdegree+x=180\textdegree$
$\therefore x=180\textdegree-56\textdegree-40\textdegree$
$\therefore x=84\textdegree$

$84\textdegree+x=180\textdegree$
$\therefore x=180\textdegree-84\textdegree$
$\therefore x=96\textdegree$

More complex examples

$90\textdegree+x=120\textdegree$ (exterior angle of a triangle)
$\therefore x=120\textdegree-90\textdegree$
$\therefore x=30\textdegree$

Another example:

$90\textdegree+38\textdegree+x=180\textdegree$ (angles of a triangle)
$\therefore x=180\textdegree-90\textdegree-38\textdegree$
$\therefore x=90\textdegree-38\textdegree$
$\therefore x=52\textdegree$

Another example:

$144\textdegree=x+2x$
$\therefore 144\textdegree=3x$
$\therefore x=48\textdegree$

Another example:

$x=x/2+47\textdegree$
$\therefore x*x=2+47\textdegree$
$\therefore x^2=\sqrt(49\textdegree)$
$\therefore x=7\textdegree$