Question

In the above figure, if AB$\parallel$CD and $\angle$APQ = 120${}^{\circ }$, what is the ratio of $\angle$APQ to $\angle$CQP?

Answer 1

We know that the angles on the same side of the transversal add up to 180${}^{\circ }$.
$\therefore$ $\angle$APQ + $\angle$CQP = 180${}^{\circ }$
$\Rightarrow$ 120${}^{\circ }$ + ​​​​​​$\angle$CQP = 180${}^{\circ }$
$\Rightarrow$ $\angle$CQP = 60${}^{\circ }$
$\therefore$ $\angle$APQ : $\angle$CQP $\Rightarrow$ 120 : 60 $\Rightarrow$ 2 : 1