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Finding one angle of a right triangle with given information

Attachment 21689

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."

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

Quote:

Originally Posted by

**KingNathan** Attachment 21689
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 ?

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

Quote:

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

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

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.

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

Quote:

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.

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

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".

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

Quote:

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.