I am currently studying for the GMAT which tests on Data Sufficiency. According to the test, I should be able to answer this question with the given statement, but I can't figure out how.
In the figure shown, the measure of angle PRS is how much greater than the measure of angle PQR?
How can I find that answer if the only information I have is this?
"The measure of angle QPR is 30 degrees."
I am struggling to find the values for angles PRQ and PQR. I am assuming that I am forgetting a rule about triangles. These are the assumptions I can draw from the information given.
Angle QPR is 30 degrees
Angle PSR is 90 degrees
Angle QPS must be larger than 30 degrees
Angle PRQ is 180 degrees-Angle PRQ
However, I can't seem to derive a value from the information given that gives me the value for neither Angle PQE nor Angle PRQ
You could work from..
Angle PRS + Angle PRQ is 180 degrees (a semicircle).
The sum of all 3 angles in triangle PQR is also 180 degrees.
One of these is Angle PRQ.
This means that Angle PRS is the sum of the other 2 angles in triangle PQR.
The question can then be answered.
The strategy here is "angles summing to 180 degrees"
and Angle PRS is common to both sums.
I apologize, and do greatly appreciate the time you are taking to help me. However, I still do not understand. I see we have only 1 angle value for each of the 2 triangles. I can't see how Angle QPR equalling 30 degrees shows us the value of any other angle in either triangle.
For convenience, label Angle PRS "A",
label Angle PRQ "B".
Then A+B = 180 degrees.
Label Angle PQR "C".
Then B+C+30 degrees = 180 degrees.
Then A=180-B
C=180-(B+30)=180-B-30
So "A" is 30 degrees bigger than "C".