Question

cdef is a kite and m∠fce = 48. find m∠3. 44 46 23 32

Explanation:

Step1: Recall kite - properties

In a kite, the diagonals are perpendicular, so $\angle 2 = 90^{\circ}$. Also, the diagonal that connects the vertices of the non - congruent angles of a kite bisects the angles at those vertices. Here, diagonal $CE$ bisects $\angle FCD$.

Step2: Use angle - sum property of a triangle

In right - triangle $FCE$, we know that $\angle FCE = 46^{\circ}$ and $\angle 2=90^{\circ}$. We want to find $\angle 3$. In $\triangle FCE$, by the angle - sum property of a triangle ($\angle 3+\angle FCE+\angle 2 = 180^{\circ}$), we can solve for $\angle 3$.
We substitute the known values into the formula: $\angle 3=180^{\circ}-\angle FCE - \angle 2$.
Since $\angle FCE = 46^{\circ}$ and $\angle 2 = 90^{\circ}$, then $\angle 3=180^{\circ}-46^{\circ}-90^{\circ}=44^{\circ}$.

Answer:

$44$