Question

if tw = vw = 85 and m∠tuw = 45°, what is m∠vuw? m∠vuw = °

Explanation:

Step1: Identify congruent right - triangles

In right - triangles $\triangle TUW$ and $\triangle VUW$, $TW = VW$ and $UW$ is common. By the Hypotenuse - Leg (HL) congruence criterion, $\triangle TUW\cong\triangle VUW$.

Step2: Use congruent - angle property

Since $\triangle TUW\cong\triangle VUW$, corresponding angles are equal. Given $m\angle TUW = 45^{\circ}$, then $m\angle VUW=m\angle TUW$.

Answer:

$45$