Question

quadrilateral tuvw is a kite. what is m∠v? m∠v =

Explanation:

Step1: Recall angle - sum property of quadrilaterals

The sum of the interior angles of a quadrilateral is $360^{\circ}$.

Step2: Let $m\angle V=x$.

We know that $m\angle W = 92^{\circ}$ and $m\angle U=78^{\circ}$. In a kite, the non - vertex angles are equal. Let's assume the sum of the four angles of the kite $TUVW$ is $m\angle T + m\angle U+m\angle V + m\angle W=360^{\circ}$. Since the non - vertex angles are equal, we have $x + 92^{\circ}+78^{\circ}+x=360^{\circ}$.

Step3: Simplify the equation

Combining like terms, we get $2x+170^{\circ}=360^{\circ}$.
Subtract $170^{\circ}$ from both sides: $2x=360^{\circ}- 170^{\circ}=190^{\circ}$.

Step4: Solve for $x$

Divide both sides by 2: $x=\frac{190^{\circ}}{2}=95^{\circ}$.

Answer:

$95$