Angles of a parallelogram

How to use it

1. 1One angle of a parallelogram determines all four: copy it to the opposite vertex and subtract it from $180^{\circ }$ at the two neighbours.
2. 2The supplementary pair is just the co-interior pair of the two parallel sides, so it survives in a trapezium for the two angles on a non-parallel side.
3. 3Halving a supplementary pair gives a complementary pair, which is why the bisectors of two consecutive angles meet at $90^{\circ }$.

Step-by-step

1. 1
   $\angle P=115^{\circ }\Rightarrow \angle R=115^{\circ }$

   Why: Opposite angles are equal.

2. 2
   $\angle Q=\angle S=180^{\circ }-115^{\circ }=65^{\circ }$

   Why: Each is consecutive to $\angle P$.