Question

if $overline{tw}congoverline{vw}$ and $mangle vuw = 61^{circ}$, what is $mangle tuv? mangle tuv=square^{circ}$

Explanation:

Step1: Identify congruent triangles

Since $\overline{TW}\cong\overline{VW}$ and $\angle T = \angle V=90^{\circ}$, and $\overline{UW}=\overline{UW}$ (common side), by the Hypotenuse - Leg (HL) congruence criterion, $\triangle TUW\cong\triangle VUW$.

Step2: Use congruent - angle property

If $\triangle TUW\cong\triangle VUW$, then corresponding angles are equal. So $\angle TUW=\angle VUW$.

Step3: Calculate $\angle TUV$

We know that $\angle TUV=\angle TUW + \angle VUW$. Given $\angle VUW = 61^{\circ}$, then $\angle TUV=2\times61^{\circ}=122^{\circ}$.

Answer:

$122$