Question

quadrilateral stuv is a kite. what is m∠v?
s 119°
u 97°
m∠v = □°

Explanation:

Step1: Recall angle - sum property of quadrilaterals

The sum of the interior angles of a quadrilateral is $360^{\circ}$. In a kite, one pair of opposite angles are equal. Here, assume $\angle V=\angle T$. Let $m\angle V = x$.

Step2: Set up an equation

We know that $m\angle S = 119^{\circ}$ and $m\angle U=97^{\circ}$, and $m\angle V = m\angle T=x$. So, $119 + 97+x + x=360$.

Step3: Simplify the equation

Combine like - terms: $216 + 2x=360$.

Step4: Solve for x

Subtract 216 from both sides: $2x=360 - 216=144$. Then divide both sides by 2: $x = 72$.

Answer:

$72$