JAMB 2000 · UME · Q25

Construction & loci
Angles, triangles & polygons

$P$ is a point on one side of the straight line $UV$ and $P$ moves parallel to $UV$ . If the straight line $ST$ is the locus of $P$ and $\angle VUS = 50^\circ$ , find $\angle UST$ .

Worked solution (try it first)

$P$ moves parallel to $UV$ , so its locus $ST$ is parallel to $UV$ , and $US$ is a transversal.
$\angle VUS$ and $\angle UST$ lie between the parallels on the same side of $US$ , so they are co-interior angles and add up to $180^\circ$ .
So $\angle UST = 180^\circ - 50^\circ$
$= 130^\circ$ , option B.

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