Rhombus
Diagonals bisect the angles of a rhombus, that is, angle Q is bisected by the diagonal and the angles are equal, thus:
4x - 27 = 2x + 7
Subtracting 2x:
4x - 2x - 27 = 7
Adding 27:
4x - 2x = 7 + 27
Operating:
2x = 34
Dividing by 2:
x = 34/2
x = 17
Now we find the measure of angle PQR:
[tex]\begin{gathered} m\angle PQR=4x-27+2x+7 \\ \text{Operating:} \\ m\angle PQR=6x-20 \end{gathered}[/tex]Substituting x=17:
[tex]m\angle PQR=6\cdot17-20=82[/tex]