Answer
$QPR \approx 48^\circ$, $PQR \approx 75^\circ$, $PRQ \approx 58^\circ$
Work Step by Step
$PQ= \lt 0-2, 3-0 \gt= \lt -2,3 \gt$
$PR= \lt 3-2, 4-0 \gt= \lt 1,4 \gt$
$|PQ|=\sqrt {13}$ and $|PR|=\sqrt {17}$
$PQ \cdot PR= \lt -2,3 \gt \cdot \lt 1,4 \gt=10$
$ \theta = cos^{-1}\dfrac{PQ \cdot PR}{|PQ||PR|}=cos^{-1}\dfrac{10}{\sqrt {221}}\approx 47.726 ^ \circ$
$QP= \lt 2-0, 0-3 \gt= \lt 2,-3 \gt$
$QR= \lt 3-0, 4-3 \gt= \lt 3,1 \gt$
$|QP|=\sqrt {13}$ and $|QR|=\sqrt {10}$
$QP \cdot QR= \lt 2,-3 \gt \cdot \lt 3,1 \gt=3$
$ \theta = cos^{-1}\dfrac{QP \cdot QR}{|QP||QR|}=cos^{-1}\dfrac{3}{\sqrt {130}}\approx 74.745 ^ \circ$
$RP= \lt 2-3, 0-4 \gt= \lt -1,-4 \gt$
$RQ= \lt 0-3, 3-4 \gt= \lt -3,-1 \gt$
$|RP|=\sqrt {17}$ and $|RQ|=\sqrt {10}$
$RQ \cdot RP= 7$
$ \theta = cos^{-1}\dfrac{RQ \cdot RP}{|RP||RQ|}=cos^{-1}\dfrac{7}{\sqrt {170}}\approx 57.529 ^ \circ$
Hence, $QPR \approx 48^\circ$, $PQR \approx 75^\circ$, $PRQ \approx 58^\circ$