Question

find ( mangle wyz ).
( x = )
( mangle wyz = )

Explanation:

Step1: Use the triangle mid - segment theorem

Since \(YZ\) is the mid - segment of \(\triangle WXV\) (because \(WY = YV\) and \(WZ=ZX\)), then \(YZ\parallel XV\). By the exterior angle property of a triangle, \(\angle WYZ=\angle WXV\). Also, we know that \(\angle WYZ=(16x - 3)^{\circ}\) and \(\angle WVX=(3x - 7)^{\circ}\). And from the property of the mid - segment and the angles formed, we have the equation \(16x-3 = 2(3x - 7)\).

Step2: Solve the equation for \(x\)

Expand the right - hand side: \(16x-3=6x - 14\).
Subtract \(6x\) from both sides: \(16x-6x-3=6x - 6x-14\), which gives \(10x-3=-14\).
Add \(3\) to both sides: \(10x-3 + 3=-14 + 3\), so \(10x=-11\) (Wait, no, there is a mistake above. The correct property is that \(\angle WYZ\) is an exterior angle. The correct equation is \(16x-3=(3x - 7)+(3x - 7)\) (because \(YZ\parallel XV\), \(\angle WYZ\) is equal to the sum of two equal angles \(\angle WVX\) (by the exterior angle theorem and parallel line properties).

The correct equation: \(16x-3 = 2(3x - 7)\)

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Step3: Calculate \(m\angle WYZ\)

Substitute \(x = 4\) into the expression for \(\angle WYZ\). If \(\angle WYZ=(16x - 3)^{\circ}\), then \(m\angle WYZ=16\times4-3\).

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Answer:

\(m\angle WYZ = 61^{\circ}\)