Question 210667
Are adjacent angles necessarily coplanar?
<pre><font size = 4 color = "indigo"><b>

You can do a "show-and-tell" with this problem:

Draw a pair of adjacent angles on a sheet of
paper like this:

{{{drawing(300,229,-1,6,-2,2,

rectangle(0,-1,4,1), line(1,0,3,.75),
line(1,0,3,0), line(1,0,3,-.75) )}}}

Those two adjacent angles are indeed coplanar.

But now let's fold the paper along their common side, like this:

{{{drawing(300,229,-1,6,-2,2,

rectangle(0,0,4,1), line(1,0,3,.75),
line(1,0,3,0), line(1,0,3.3,-.25),
line(0,0,1,-.5), line(4,0,5,-.5), line(1,-.5,5,-.5) 

)}}}

and you can see the two angles are still adjacent,
however they are in two different planes.  Therefore
the answer is: 

<i><u>Adjacent angles are not necessarily coplanar.</i></u>

Edwin</pre>