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1.3.2 Exterior angle




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

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