Question

quadrilateral efgh is a kite. what is m∠e? m∠e = °

Explanation:

Step1: Recall angle - sum property of a quadrilateral

The sum of the interior angles of a quadrilateral is $360^{\circ}$. In a kite, one pair of opposite angles are equal. Here, assume $\angle F$ and $\angle H$ are non - equal angles, and $\angle E=\angle G$.

Step2: Set up an equation

Let $m\angle E = m\angle G=x$. We know that $m\angle F = 63^{\circ}$ and $m\angle H=41^{\circ}$. Then, by the angle - sum property of a quadrilateral, $x + x+63^{\circ}+41^{\circ}=360^{\circ}$.

Step3: Simplify the equation

Combining like terms, we get $2x+104^{\circ}=360^{\circ}$.

Step4: Solve for $x$

Subtract $104^{\circ}$ from both sides: $2x=360^{\circ}- 104^{\circ}=256^{\circ}$. Then divide both sides by 2: $x=\frac{256^{\circ}}{2}=128^{\circ}$.

Answer:

$128$