how to annotate the following trapezoid picture?

Question

I have this trapezoid in Tikz, and I would like to put some text inside the trapezoid, next to the angles, and also place next to each vertex, outside of the trapezoid, one of the letters A,B,C,D. I have a feeling I need to annotate (0,0) etc. for all of this, but not sure how and how to set the placement. Any ideas?

 \begin{tikzpicture}
 \newdimen\R
 \R=1cm
  \newdimen\S
   \S=1.5cm
    \draw[xshift=10.5\R] (0,0) -- (2.8\S,0) 
    -- node[rotate=-52]{} (2\S,1.1\S) -- (.8\S,1.1\S)
    -- node[rotate=52]{} (0,0);
    \draw[xshift=10.5\R] (1.4\S,-.5) node {}
    ++ (0,-.5) node {};
 \end{tikzpicture}

Answer 1

If you don't have to use the code you already have, there is a trapezium node shape available, in the shapes.geometric library.

\documentclass[tikz]{standalone}
\usetikzlibrary{shapes.geometric}
\begin{document}
\begin{tikzpicture}
  \node (a)
  [shape=trapezium,
  trapezium left angle=70,
  trapezium right angle=45,
  draw,
  minimum height=1.1*1.5cm] {Inside};
  \node [above left] at (a.top left corner) {A};
 \node [above right] at (a.top right corner) {B}; 
 \node [below left] at (a.bottom left corner) {C};
 \node [below right] at (a.bottom right corner) {D}; 

 \node [below right] at (a.top left corner) {$\alpha$};
 \node [below left] at (a.top right corner) {$\beta$}; 
 \node [above right] at ([xshift=.2cm]a.bottom left corner) {$\gamma$};
 \node [above left] at ([xshift=-.3cm]a.bottom right corner) {$\varphi$}; 

\end{tikzpicture}
\end{document}