Question

question
in △vwx, $overline{vw}congoverline{xv}$ and m∠v = 47°. find m∠x.

Explanation:

Step1: Identify isosceles - triangle

Since $\overline{VW}\cong\overline{XV}$, $\triangle VWX$ is an isosceles triangle with base - angles equal. $\angle W$ and $\angle X$ are base - angles.

Step2: Use angle - sum property of a triangle

The sum of the interior angles of a triangle is $180^{\circ}$. Let $m\angle X = m\angle W=x$. Then $m\angle V + m\angle W + m\angle X=180^{\circ}$. Given $m\angle V = 47^{\circ}$, we have $47^{\circ}+x + x=180^{\circ}$.

Step3: Solve for $x$

Combining like terms, $47^{\circ}+2x = 180^{\circ}$. Subtract $47^{\circ}$ from both sides: $2x=180^{\circ}- 47^{\circ}=133^{\circ}$. Then divide both sides by 2: $x=\frac{133^{\circ}}{2}=66.5^{\circ}$.

Answer:

$m\angle X = 66.5^{\circ}$