Question

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

Explanation:

Step1: Identify the triangle type

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

Step2: Use the angle - sum property of a triangle

The sum of the interior angles of a triangle is $180^{\circ}$. Let $m\angle U = x$ and $m\angle V=x$ (because base - angles of an isosceles triangle are equal), and $m\angle W = 51^{\circ}$. Then $x + x+51^{\circ}=180^{\circ}$.

Step3: Solve the equation for $x$

Combine like terms: $2x+51^{\circ}=180^{\circ}$. Subtract $51^{\circ}$ from both sides: $2x=180^{\circ}- 51^{\circ}=129^{\circ}$. Divide both sides by 2: $x=\frac{129^{\circ}}{2}=64.5^{\circ}$.

Answer:

$64.5^{\circ}$