Answer
Equilateral triangle
Work Step by Step
$\angle$BCE=$\frac{1}{2}$$\angle$C
$\angle$B+$\angle$C=180
$\angle$B+$\angle$BCE+$\angle$BEC=180
$\angle$B+$\frac{1}{2}$$\angle$C+$\angle$BEC=180
$\angle$B+$\frac{1}{2}$$\angle$C+$\angle$BEC=$\angle$B+$\angle$C
$\angle$BEC=$\frac{1}{2}$$\angle$C
Since two angles have a measure equal to half of angle C, it must be an equilateral triangle.
