Question

question
in △uvw, $overline{vw}congoverline{uv}$ and m∠v = 159°. find m∠u.

Explanation:

Step1: Identify isosceles - triangle

Since $\overline{VW}\cong\overline{UV}$ in $\triangle UVW$, $\triangle UVW$ is an isosceles triangle. So $\angle U=\angle W$.

Step2: Use angle - sum property

The sum of interior angles of a triangle is $180^{\circ}$. Let $m\angle U = x$ and $m\angle W=x$. We know $m\angle V = 159^{\circ}$. Then $x + x+159^{\circ}=180^{\circ}$.

Step3: Solve for $x$

Combining like - terms gives $2x=180^{\circ}- 159^{\circ}=21^{\circ}$. Dividing both sides by 2, we get $x=\frac{21^{\circ}}{2}=10.5^{\circ}$.

Answer:

$10.5^{\circ}$