Question

cdef is a kite and m∠fce = 48. find m∠3

Explanation:

Step1: Recall kite - properties

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

Step2: Use angle - sum property of a triangle

In right - triangle $FCE$, we know that the sum of the interior angles of a triangle is $180^{\circ}$. Given $\angle FCE=46^{\circ}$ and $\angle 2 = 90^{\circ}$, and we want to find $\angle 3$.
We use the formula $\angle 3=180^{\circ}-\angle 2 - \angle FCE$.
Substitute $\angle 2 = 90^{\circ}$ and $\angle FCE = 46^{\circ}$ into the formula:
$\angle 3=180^{\circ}-90^{\circ}-46^{\circ}=44^{\circ}$

Answer:

$44$