SOLUTION: In triangle PQR, X is a point on QR such that angle RPX = angle Q. Prove that angle PXR = angle QPR

Question 1162497: In triangle PQR, X is a point on QR such that angle RPX = angle Q. Prove that angle PXR = angle QPR
Answer by Edwin McCravy(20060) (Show Source): You can put this solution on YOUR website!



We are to prove that the angles with the green arcs are equal, 

∠PXR = ∠QPR

given

that the angles with the red arcs are equal,

∠RPX = ∠Q

We use the fact that the three internal angles of a triangle have sum 180°,

For ΔPQR, 

(1)  ∠QPR + ∠R + ∠Q = 180°. Therefore,

(2)  ∠QPR = 180° - ∠R - ∠Q

For ΔRPX, 

(3)  ∠PXR + ∠R + ∠RPX = 180°. Therefore, 

(4)  ∠PXR = 180° - ∠R - ∠RPX 

Since we are given that ∠RPX = ∠Q, the right sides
of (2) and (4) are equal, so their left sides are also equal. 
Therefore,

∠PXR = ∠QPR

Now you can write that up in a two-column proof.

Edwin

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