Let's draw a diagram and highlight the angles we are asked to compare.
We also should label the vertices of the triangles on the diagram.
Let's identify congruent segments in the triangles corresponding to the different positions of the locker doors.
Congruent Segments
Justification
MN≅RS
Both segments represent the width of the locker.
NP≅ST
Both segments represent the width of the locker door in different positions.
Using the measures on the diagram, we can compare the length of the segments MP and RT.
12<17
⇓
MP< RT
Since triangles △ NPM and △ STR have two pairs of congruent sides, the Converse of the Hinge Theorem allows us to compare the included angles.
MP< RT
⇓
m ∠ MNP
