Question

question
in △uvw, $overline{uv}congoverline{wu}$ and m∠w = 51°. find m∠u.

Explanation:

Step1: Identify isosceles - triangle

Since $\overline{UV}\cong\overline{WU}$, $\triangle UVW$ is an isosceles triangle. In an isosceles triangle, the base - angles are equal. So $\angle V=\angle W$.

Step2: Use angle - sum property of a triangle

The sum of the interior angles of a triangle is $180^{\circ}$. Let $m\angle U = x$, $m\angle V = m\angle W=51^{\circ}$. Then $x + 51^{\circ}+51^{\circ}=180^{\circ}$.

Step3: Solve for $m\angle U$

$x=180^{\circ}-(51^{\circ}+51^{\circ})=180^{\circ}-102^{\circ}=78^{\circ}$.

Answer:

$78^{\circ}$