Note that the sum of the angles in a triangle is 180 degrees
Since we already have the measurement of two angles :
59 and 46
The third angle will be :
[tex]180-59-46=75[/tex]
So we have :
[tex]\begin{gathered} \angle P=59 \\ \angle Q=46 \\ \angle R=75 \end{gathered}[/tex]
Note that the sides opposite to the angles are :
[tex]\begin{gathered} \angle P\rightarrow\overline{QR} \\ \angle Q\rightarrow\overline{PR} \\ \angle R\rightarrow\overline{PQ} \end{gathered}[/tex]
Also note that, the measurement of the sides are proportional to their corresponding angles.
Since :
[tex]\angle Q<\angle P<\angle R[/tex]
The sides are :
[tex]\overline{PR}<\overline{QR}<\overline{PQ}[/tex]
Therefore the correct order from longest to shortest is :
PQ - QR - PR
