Answer:
C. 52°
Step-by-step explanation:
The question lacks the required diagram. Find the diagram attached below.
Since all the sides and angles of a rhombus are the same, hence, all the right angled triangle in each quadrant are also the same.
From the diagram, < XWZ = < XWV + < VWZ and < XWV = < VWZ
Therefore < XWZ = < VWZ + < VWZ
< XWZ = 2<VWZ
let us calculate the angle <VWZ first.
From ΔVWZ, <WVZ +<WZV + <VWZ = 180°... 1
From the diagram <WVZ = 90°, <WZV = <VZY = 64°
On substituting into 1
90°+64°+ <VWZ = 180°
154°+ <VWZ = 180°
<VWZ = 180°-154°
<VWZ = 26°
Since < XWZ = 2<VWZ
< XWZ = 2(26°)
< XWZ = 52°
Hence the measure of < XWZ is 52°
