Question

what is the value of z?
u (arrow left), v (arrow up), x (arrow down), w. triangle uvw with right angle at v, side uv is z+4. triangle uxw with right angle at x, side ux is 3z. angle at w for both triangles is 50 degrees.
z =
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Explanation:

Step1: Identify congruent triangles

Triangles \( UVW \) and \( UXW \) are congruent (by AAS: right angles, \( \angle VWU = \angle XWU = 50^\circ \), and common side \( UW \)). So their corresponding sides are equal.
Thus, \( z + 4 = 3z \).

Step2: Solve for \( z \)

Subtract \( z \) from both sides: \( 4 = 2z \).
Divide both sides by 2: \( z = \frac{4}{2} = 2 \).

Answer:

\( z = 2 \)