Question

1. find m\angle wyz

Explanation:

Step1: Use the triangle - proportionality theorem

Since \( YZ\parallel VX\), by the basic - proportionality theorem (Thales' theorem), \(\frac{WY}{YV}=\frac{WZ}{ZX}\). Given \( WY = 2\), \(YV=2\), \(WZ = 3\), \(ZX = 3\). Also, by the angle - angle similarity (because \( YZ\parallel VX\), \(\angle WYZ=\angle WVX\) and \(\angle WZY=\angle WXV\)), \(\triangle WYZ\sim\triangle WVX\). And \(\angle1=\angle2\) (corresponding angles for parallel lines \( YZ\parallel VX\) and transversal \( VW\)).

We know that \(\angle1+\angle5+\angle2=(16x - 37)+(3x - 7)+(3x - 7)=180\) (angle - sum property of a triangle, \(\angle1=\angle2 = 3x - 7\) and \(\angle5=16x-37\)).

Step2: Solve the equation for \(x\)

Combine like terms: \((16x+3x + 3x)-(37 + 7+7)=180\).
\(22x-51 = 180\).
Add \(51\) to both sides: \(22x=180 + 51=231\).
Divide both sides by \(22\): \(x=\frac{231}{22}=10.5\).

Step3: Find \(\angle WYZ\)

Since \(\angle WYZ=\angle2\) (because \( YZ\parallel VX\), alternate - interior angles are equal). Substitute \(x = 10.5\) into \(\angle2=(3x - 7)\).
\(\angle WYZ=3\times10.5-7\).
\(=31.5-7\).
\(=24.5\)

Answer:

\(24.5\)