Hello,

I am having trouble with the following problem. I don't understand how angle QPR is sufficient to answer the question. Please enlighten me :shock:

PRS = QPR + PQR (exterior angle of a triangle is equal to sum of two interior angles)
PRS - PQR = QPR = 30. (1) is sufficient.
(2) provides the same information as (1).

Hence, (D).

-givemeanid

I forgot about that rule! It makes sense now :)

givemeanid has got it! You do need to make sure you know that exterior angle rule to get a high score on the test. :)

Does this rule only apply to right triangles?

Nope, external angle rule applies to any triangles.

eh, the exterior angle rule is nice, but you don't need it to address this question.
in fact, you don't ever need the exterior angle rule; anything you can do with that rule, you can also do in a more roundabout fashion by just using the combination of two very basic facts: (1) 180° in a triangle, (2) 180° in a straight line.
granted, that approach will take longer than the exterior angle approach, but the exterior angle approach is only shorter if you think to use it right away. if you don't recognize the opportunity to use the exterior angle theorem RIGHT AWAY, then don't bother with it; just use 180° in a straight line and 180° in a triangle instead. just be prepared to deal with some pretty nasty algebra in some cases.

in this problem:
let angle QPR = 30°
let angle RPS = x°

then
using triangle PRS, we have x + 90 + angle PRS = 180°
so, angle PRS = (90 - x)°

using triangle PQS, we have (x + 30) + 90 + angle PQS = 180°
so, angle PQS = (60 - x)°

now (90 - x) is greater than (60 - x) by a margin of exactly thirty, so this is sufficient to answer the problem.

notice that the exterior angle theorem isn't necessary to do this, although it certainly makes for a shorter and more elegant solution. don't sweat it too hard, though; unless you're really weak in algebra, it's not an essential piece of knowledge.
remember that there are no style points.