WAEC 2020 · Paper 1 · Q30

In the diagram, $MN \parallel PQ$ , $\angle MNP = 2x$ and $\angle NPQ = (3x - 50)^\circ$ . Find the value of $\angle NPQ$ .

Worked solution (try it first)

$MN \parallel PQ$ and $\angle MNP$ , $\angle NPQ$ are alternate angles, so they are equal: $2x = 3x - 50$ .
Subtract $2x$ and add 50: $x = 50$ .
So $\angle NPQ = 3(50) - 50 = 100^\circ$ , option D.