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Senior Manager
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I am not sure how to insert a picture, so have attached a [#permalink] New post 15 Nov 2008, 22:46
I am not sure how to insert a picture, so have attached a file.

The measure of angle PRS is how many degrees greater than the measure of angle PQR?

1. QPR = 30 deg
2. PQR + PRQ = 150 deg
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Re: Geometry- [#permalink] New post 15 Nov 2008, 23:26
The question stem asks "PRS - PQR = ?" It can be converted to

PRS - PQR = (QPR + PQR) - PQR
= QPR

1. QPR = 30 degree => Sufficient
2. PQR + PRQ = 150 degree => This implies that QPR = 30 degree => Sufficient

IMO: D
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Re: Geometry- [#permalink] New post 16 Nov 2008, 01:13
would you please explain the logic:

PRS - PQR = (QPR + PQR) - PQR

Why would you add and deduct PQR. Basically your statement simply means that PRS - PQR = PQR, but how do you get to that?

Any takers?
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Re: Geometry- [#permalink] New post 16 Nov 2008, 02:59
i think it is E
1) QPR=30 does not take us anywhere, insuff...
2) PQR+PRQ=150, but we do not know how many degrees is each angle... insuff
taken together, once again we do not what is PQR or QRP
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Re: Geometry- [#permalink] New post 16 Nov 2008, 03:22
study wrote:
would you please explain the logic:

PRS - PQR = (QPR + PQR) - PQR

Why would you add and deduct PQR. Basically your statement simply means that PRS - PQR = PQR, but how do you get to that?

Any takers?



PRS = (180 - PRQ) ---- (1)

But PQR + PRQ + QPR = 180
PRQ = 180 - PQR - QPR ---- (2) ---> Substitute in (1)

PRS = [180 - (180 - PQR - QPR)] = PQR + QPR

Therefore, according to the question stem,

PRS - PQR = (PQR + QPR) - PQR
= QPR
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Re: Geometry- [#permalink] New post 17 Nov 2008, 02:43
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Hope this helps:

Ref: Triangle PQR angles measure 180 deg
Angle PRQ = x
Angle QPR = 30 (given)
Hence, Angle PQR = 180 - (30+x)

Ref: QRS is a straight line
Angle PRQ = x
Hence, Angle PRS = 180 - x

Difference between PQR and PRS
(180 - x) - (180 - 30 -x)
180 - 150 = 30
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Re: Geometry- [#permalink] New post 15 Feb 2009, 22:06
study wrote:
Hope this helps:

Ref: Triangle PQR angles measure 180 deg
Angle PRQ = x
Angle QPR = 30 (given)
Hence, Angle PQR = 180 - (30+x)

Ref: QRS is a straight line
Angle PRQ = x
Hence, Angle PRS = 180 - x

Difference between PQR and PRS
(180 - x) - (180 - 30 -x)
180 - 150 = 30


This helps a lot! Thanks.
Re: Geometry-   [#permalink] 15 Feb 2009, 22:06
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