Question

what is the value of z? z =

Explanation:

Step1: Apply the Angle - Bisector Theorem (HL Congruence for right - angled triangles)

Since \(WY\) is the angle bisector (\(\angle XWY=\angle VWY = 50^{\circ}\)) and \(YX\perp WX\), \(YV\perp WV\) (right angles), by the Hypotenuse - Leg (HL) congruence criterion for right - angled triangles, the two right - angled triangles \(\triangle WXY\) and \(\triangle W VY\) are congruent. So, the lengths of the corresponding sides are equal. That is, \(z + 54=3z\).

Step2: Solve the equation for \(z\)

Subtract \(z\) from both sides of the equation \(z + 54=3z\).
We get \(54=3z - z\).
Simplify the right - hand side: \(54 = 2z\).
Divide both sides by 2: \(z=\frac{54}{2}\).

Answer:

\(27\)