What is the measure of ∠WZX in rhombus WXYZ? Rhombus W X Y Z has segments connecting X to Z and W to Y. Angle Y W X is 77 degrees and angle Y W Z is congruent to Y W X.

A.38.5

B.51.5

C.77

D.103

WZY= 13

Explanation:

Given

Rhombus WXYZ (See attachment for diagram)

Note that: Rhombus in the attachment is not drawn to scale

<YWX = 77

Required

Find <WZX

Given that <YWZ is congruent to <YWX;

<YWZ = <YWX = 77

Since opposite sides of a rhombus are parallel; then

<YWZ = <ZYX = 77

Let the center of the Rhombus be represented by P

<P = 90 (ZX and WY are perpendicular lines)

In Triangle PWZ

The sum of angles in a triangle is 180;

So,

<PWZ + <WZP + <P = 180

Substitute <P = 90; <PWZ = 77;

77 + <PZW + 90 = 180

Collect like terms

90 + 77 + <WZP = 180

167 + <WZP = 180

Subtract 167 from both sides

167 - 167 + <WZP = 180 - 167

<WZP = 13

Since line ZP extends to ZX;

<WZX = <WZP = 13

Hence, <WZX = 13;