Question

quadrilateral tuvw is a kite. what is m∠w? m∠w = °

Explanation:

Step1: Recall kite - angle property

In a kite, one pair of opposite angles are equal. Here, $\angle V$ and $\angle T$ are not the equal - pair. Let $\angle W$ and $\angle U$ be the equal - pair of angles.

Step2: Use the angle - sum property of a quadrilateral

The sum of the interior angles of a quadrilateral is $360^{\circ}$. So, $m\angle V + m\angle T+m\angle W + m\angle U=360^{\circ}$. Since $m\angle W = m\angle U$, we can rewrite it as $57^{\circ}+71^{\circ}+2m\angle W=360^{\circ}$.

Step3: Simplify the equation

First, add the known angles: $57 + 71=128$. The equation becomes $128^{\circ}+2m\angle W=360^{\circ}$.

Step4: Solve for $m\angle W$

Subtract $128^{\circ}$ from both sides: $2m\angle W=360^{\circ}-128^{\circ}=232^{\circ}$. Then divide both sides by 2: $m\angle W = 116^{\circ}$.

Answer:

$116$