Answer:
[tex]m\angle WXY=127^{o}[/tex]
Step by step explanation:
We have been given that in kite [tex]m\angle XWY=38^{o}[/tex] and [tex]m\angle ZYW=15^{o}[/tex]. We are asked to find measure of angle WXY.
Since we know that the diagonal of symmetry divides kite into two congruent triangles and it also bisects the pair of opposite angles.
We can see from our diagram that WY is the diagonal of symmetry so [tex]m\angle XWY=m\angle ZWY[/tex] and [tex]m\angle XYW=m\angle ZYW[/tex].
First of all we will find measure of angle XYW.
[tex]m\angle XYW=m\angle ZYW[/tex]
[tex]m\angle XYW=15^{o}[/tex]
In our triangle WXY we know measures of two angles and we will find measure of angle WXY using angle sum property of triangles.
[tex]m\angle XYW+m\angle XWY+m\angle WXY=180^{o}[/tex]
Upon substituting our given values we will get,
[tex]15^{o}+38^{o}+m\angle WXY=180^{o}[/tex]
[tex]53^{o}+m\angle WXY=180^{o}[/tex]
[tex]m\angle WXY=180^{o}-53^{o}[/tex]
[tex]m\angle WXY=(180-53)^{o}[/tex]
[tex]m\angle WXY=127^{o}[/tex]
Therefore, [tex]m\angle WXY\text{ will be }127^{o}[/tex].
