Thread: Finding one angle of a right triangle with given information

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."

Originally Posted by KingNathan

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."

Angle PRS is the external angle of triangle PQR.
Angle PRS is the sum of which 2 angles in triangle PQR ?

Originally Posted by Archie Meade

Angle PRS is the external angle of triangle PQR.
Angle PRS is the sum of which 2 angles in triangle PQR ?

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.

Originally Posted by Archie Meade

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".

Originally Posted by Archie Meade

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".

Awesome! Thanks for your help.