Question

question
in △uvw, $overline{uv}congoverline{wu}$ and m∠w = 38°. find m∠u.

Explanation:

Step1: Identify the triangle type

Since $\overline{UV}\cong\overline{WU}$, $\triangle UVW$ is isosceles. In an isosceles triangle, base - angles are equal. $\angle V$ and $\angle W$ are base - angles. So $\angle V=\angle W = 38^{\circ}$.

Step2: Use the angle - sum property of a triangle

The sum of the interior angles of a triangle is $180^{\circ}$. Let $m\angle U=x$. Then $x + m\angle V+m\angle W=180^{\circ}$. Substitute $m\angle V = 38^{\circ}$ and $m\angle W = 38^{\circ}$ into the equation: $x+38^{\circ}+38^{\circ}=180^{\circ}$.

Step3: Solve for $m\angle U$

First, simplify the left - hand side: $x + 76^{\circ}=180^{\circ}$. Then subtract $76^{\circ}$ from both sides: $x=180^{\circ}-76^{\circ}=104^{\circ}$.

Answer:

$104^{\circ}$