Question

in $\triangle uvw$, $\overline{uv} \cong \overline{wu}$ and $m\angle w = 51^\circ$. find $m\angle u$.

Explanation:

Step1: Identify triangle type

Since $\overline{UV} \cong \overline{WU}$, $\triangle UVW$ is isosceles with base $\overline{VW}$. The base angles opposite the congruent sides are $\angle W$ and $\angle V$.

Step2: Set base angles equal

$\text{m}\angle W = \text{m}\angle V = 51^\circ$

Step3: Sum angles to 180°

The sum of angles in a triangle is $180^\circ$. Let $\text{m}\angle U = x$.
$$x + 51^\circ + 51^\circ = 180^\circ$$

Step4: Solve for $x$

$$x = 180^\circ - 102^\circ = 78^\circ$$

Answer:

$78^\circ$