Question 1134178
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<pre>
It is very easy to solve.


You are given that the angle YWZ is 43 degrees.


Hence, the angle ZWX has the measure which is TWO TIMES the measure of the angle YWZ, i.e. 86 degrees 
(since the diagonal WZY of the rhombus WXYZ bisects its angle W).



Next, since the angle ZWX (which is exactly the angle W at the vertex W of the rhombus) is 86 degrees,

then the angle WXY of the rhombus (which is the angle at the vertex X of the rhombus) is 180 - 86 = 94 degrees

It is because any two consecutive (= adjacent) interior angles of each rhombus are supplementary.



The last step is to notice that the angle ZXW is HALF of the angle WXY (diagonals of the rhombus bisect its angles).

Hence, the angle ZXW measure is 94/2 = 47 degrees.     <U>ANSWER</U>
</pre>

Completed and Solved.


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On properties of rhombis, see the lessons

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Parallelograms/Diagonals-of-a-rhombus-are-perpendicular.lesson>Diagonals of a rhombus are perpendicular</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Parallelograms/Diagonals-of-a-rhombus-bisect-its-angles.lesson>Diagonals of a rhombus bisect its angles</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/geometry/The-length-of-diagonals-of-a-rhombus.lesson>The length of diagonals of a rhombus</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/geometry/A-circle-inscribed-to-the-rhombus.lesson>A circle inscribed in the rhombus</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/geometry/How-to-solve-problems-on-the-rhombus-sides-and-diagonals-measures-Examples.lesson>HOW TO solve problems on the rhombus sides and diagonals measures - Examples</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/geometry/The-length-of-diagonals-of-a-rhombus.lesson>The length of diagonals of a rhombus</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Parallelograms/PROPERTIES-OF-RHOMBIS.lesson>PROPERTIES OF RHOMBIS</A>

in this site.


Also, &nbsp;you have this free of charge online textbook on Geometry

&nbsp;&nbsp;&nbsp;&nbsp;<A HREF=https://www.algebra.com/algebra/homework/Triangles/GEOMETRY-your-online-textbook.lesson>GEOMETRY - YOUR ONLINE TEXTBOOK</A> 

in this site.


The referred lessons are the part of this textbook under the topic "<U>Properties of rhombis</U>".



Save the link to this online textbook together with its description


Free of charge online textbook in GEOMETRY
https://www.algebra.com/algebra/homework/Triangles/GEOMETRY-your-online-textbook.lesson


to your archive and use it when it is needed.