statement 1: angle QPR = 30

angle prs = angle qpr + angle qpr (exterior angle = sum of interior opposite angles)

angle prs-angle qpr = 30

sufficient

statement 2: angle pqr + angle prq =150

therefore angle QPR = 30

angle prs = angle rps + angle qpr (exterior angle = sum of interior opposite angles)

angle prs-angle QPR = 30

sufficient

IMO D

Look into this thread

https://www.beatthegmat.com/gmat-prep-qu ... 13176.html

These questions are really algebra questions related to the core concept in DS that if the number of variables equals the number of equations you can solve the problem.

Here you have 3 triangles and one straight line (QRS)- and you have 5 variables - (angle Q, QRS, RPQ, RPS, SRP - we know that s=90) Each triange has a formula that says the sum of its angles =180 and the line says the sum of its angles is also 180. Therefore you have 5 variables and 4 formulas - all you need to be able to solve is one more formula.

each of the answer choices gives you an additional formula so each is sufficient on its own - Answer D (by the way I've seen this problem with 7 triangles and it is the exact same problem.)

Thanks Becky Selango and Krazy ...
Actually, I looked for this question, but found nothing .. maybe because it was an image embeded, and I looked for a text ... Anyway, Krazy, you're explanation is more than clear ...
And Becky, I'll watch carefully every image I see ...
Thanks
Silvia