Trapezoid Arch and Panel Design Problem - Problem 2   A common
application of isosceles trapezoids is the arch problem. In this
problem I’m telling you that all trapezoids are congruent and
isosceles, so I’m going to mark all of these sides as being
congruent and we’re trying to find angles x and y. So to do this
we need a game plan. So let’s take a look at a good game plan of
how to find these angles.  Well the first step to is to realize
that you only see half of a polygon here. That there is actually
a whole bunch of sides down below because when you build an
arch, you’re not going to build part of it underground, but you
do have to count these as part of a whole polygon.  The reason
why that’s important is that if you zoomed in on one of these
intersections here, it would look something like this and you
see that if we can find this interior angle of the polygon, then
we can find our base angles x.  So the key thing here is to use
our formula for finding the interior angle of the polygon which
is 180 time