Question

if \\(\overline{st} \cong \overline{sv}\\) and \\(m\angle sut = 56^\circ\\), what is \\(m\angle tuv\\)?
\\(m\angle tuv = \square^\circ\\)

Explanation:

Step1: Identify congruent triangles

$\triangle STU$ and $\triangle SVU$ are right triangles with $\overline{ST} \cong \overline{SV}$ and shared side $\overline{SU}$, so $\triangle STU \cong \triangle SVU$ (HL congruence).

Step2: Find $\angle SUV$

Corresponding angles of congruent triangles are equal, so $m\angle SUV = m\angle SUT = 56^\circ$.

Step3: Calculate $\angle TUV$

$m\angle TUV = m\angle SUT + m\angle SUV$
$m\angle TUV = 56^\circ + 56^\circ$

Answer:

$112^\circ$