1 Answer

Jared Chu · Answer 1 · 2023-10-14T23:36:04+0000

It is given that

$\angle XWY=u-44^o,\text{ and }\angle YZW=110^o$

Recall that the adjacent angles are supplementary in a rhombus.

$\angle XWZand\text{ }\angle YZW\text{ are supplementary angles.}$

The sum of supplementary angles is 180 degrees.

$\angle XWZ+\angle YZW=180^o\text{.}$

$Substitute\text{ }\angle YZW=110^o,\text{ we get}$

$\angle XWZ+110^o=180^o\text{.}$

$\angle XWZ=180^o-110^o$

$\angle XWZ=70^o$

$\angle XWZ=\angle XWY+\angle YWZ$

Recall that the diagonals bisect the angles of the rhombus.

$\angle XWY=\angle YWZ$

$\angle XWZ=\angle XWY+\angle XWY$

$\angle XWZ=2\angle XWY$

$Substitute\text{ }\angle XWZ=70^o\text{ and }\angle XWY=u-44^o,\text{ we get}$

Hence the value of u=79 degrees.

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