It is given that
[tex]\angle XWY=u-44^o,\text{ and }\angle YZW=110^o[/tex]
Recall that the adjacent angles are supplementary in a rhombus.
[tex]\angle XWZand\text{ }\angle YZW\text{ are supplementary angles.}[/tex]
The sum of supplementary angles is 180 degrees.
[tex]\angle XWZ+\angle YZW=180^o\text{.}[/tex]
[tex]Substitute\text{ }\angle YZW=110^o,\text{ we get}[/tex]
[tex]\angle XWZ+110^o=180^o\text{.}[/tex]
[tex]\angle XWZ=180^o-110^o[/tex]
[tex]\angle XWZ=70^o[/tex]
[tex]\angle XWZ=\angle XWY+\angle YWZ[/tex]
Recall that the diagonals bisect the angles of the rhombus.
[tex]\angle XWY=\angle YWZ[/tex]
[tex]\angle XWZ=\angle XWY+\angle XWY[/tex]
[tex]\angle XWZ=2\angle XWY[/tex]
[tex]Substitute\text{ }\angle XWZ=70^o\text{ and }\angle XWY=u-44^o,\text{ we get}[/tex]
[tex]70^o=2(u-44^0)[/tex]
[tex]\frac{70^o}{2}=u-44^0[/tex]
[tex]35^o=u-44^0[/tex]
[tex]35^o+44^o=u[/tex][tex]u=79^o[/tex]
Hence the value of u=79 degrees.
