Which angle has the same measure as angle N?
A) $\displaystyle angle$LKT
B) $\displaystyle angle$NLM
C) $\displaystyle angle$NML
D) $\displaystyle angle$LTK
Are you just supposed to eyeball this?
I'm not familiar with the way of describing angles like that, but...
angle N = angle T
since line NM and line KT are parallel. (you can see that because of those small squares, those means 90 degrees...)
I guess Sara in the example wanted to find the width of the river? So its a bit weird asking for the angle?
In addition to "eyeballing" thinking helps!
You have two right triangles so you know the two non-right angles in each triangle must add to 90. Further, it should be clear that angles MLN and KLT are the same. What does that tell you about angles LMN and LTK?
The problem didn't ask for the angle, just to show that two angles are the same. And, since all the angles are the same, the triangles are "similar" which means that corresponding sides are in the same proportion:
$\displaystyle \frac{TK}{MN}= \frac{KL}{LM}$. Since MN, KL, and LM can be measured on the same side of the river, TK can be solved for.