So angle B= angle e.
The second equation can be obtained by paralleling two groups of opposite sides respectively and then using the properties of parallelogram.
or
Let PN and BC intersect at d, because MP//BC, so angle P+ angle BDP= 180, angle P= 180- angle BDP.
Because AB//PN, angle B+ angle BDP= 180 and angle B= 180- angle BDP, angle B= angle p.
The third is equality and complementarity. Let RS and BC intersect D. According to AB//RS, angle ABC+ angle BDR= 180, and because BC//TS and angle BDR=TSR, angle B+ angle S= 180.