I've been excited because she's starting geometry, and I really like the subject. So I am presented with this (I'm reconstructing) as the first problem.
There are so many things wrong with this that it's hard to know where to start. The biggest one is that she has not previously seen a problem like this being solved. The idea seems to be that students learn best when they figure everything out for themselves. Naturally, she's lost.
The second major issue is that whoever designed this curriculum thinks that in studying geometry, the student should spend most of the time practicing the skills from previous years. Hence the injection of algebra and arithmetic into this problem, where it really does not belong.
Beyond that, there is a misplaced emphasis on exact calculation, as if the measure of angles is the heart of the subject.
And there is a pedantic distinction between the name of an angle and its measure. Granted, this is a distinction worth being made, but then, move on. There is no harm and great simplification in using the name to refer to both things.
This creeps into the discussion in other ways. In the next problem, the phrase linear pair is insisted upon, as if distinguishing the case where two angles add up to two right angles (I mean, 180°) really matters. It's that misplaced emphasis on calculation again.
They insist on using the classical notation invented by the Greeks. As everyone knows, it's confusing to constantly refer back to a diagram and then say, now was that angle ABC or CBD? It is so much better to use θ and φ, or even, gasp, s and t. Having the right notation frees the mind to think about what's important.
The geometry content of this question can be reduced to restating the definition: to bisect an angle means to cut it in half. The two resulting parts have equal measure. Even better, show how the construction can be done, and then, have a discussion about why it works.
Now, that's worth talking about.
