Question

if ∠tvu ≅ ∠tvw and tw = 30, what is tu?

Explanation:

Step1: Identify congruent triangles

Since $\angle TVU\cong\angle TVW$, $\angle TUV = \angle TWV=90^{\circ}$ and $TV$ is common to both $\triangle TUV$ and $\triangle TWV$. By the Angle - Angle - Side (AAS) congruence criterion, $\triangle TUV\cong\triangle TWV$.

Step2: Use property of congruent triangles

For congruent triangles $\triangle TUV$ and $\triangle TWV$, corresponding sides are equal. So $TU = TW$.

Answer:

$30$