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triangles- please help

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by DanaJ » Wed Mar 11, 2009 9:02 am
First off, let's make some observations:
PRQ = 180 - (QPR + PQR).
In turn, PRQ + PRS = 180, which means that:
180 - (QPR + PQR) + PRS = 180
PRS - (QPR + PQR) = 180
PRS - PQR = QPR.
This means that calculating the difference between the two angles comes down to calculating QPR.

1. provides exactly the measurement of QPR, which is the required difference. So this one is sufficient.

2. Since PQR is a triangle, the sum of its angles will be 180, meaning that PQR + PRQ + QPR = 180. Use the info provided in 2 to establish that QPR = 180 - (PQR + PRQ) = 180 - 150 = 30, and again we have everything we need. So 2 is sufficient as well.

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