Quadrilateral WXYZ is a rhombus. What is the measure of < XWZ? A)64
B)26
C)52
D)32

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°

answer: the value of x is 7cm

step-by-step explanation: