we are given the following measurements for two angles of a triangle
[tex]\begin{gathered} m\angle A=67 \\ m\angle D=54 \end{gathered}[/tex]
We are asked to find the measure of angle E. Since angle E belongs to the same triangle, if we add the measure of the three angles the result must be 180, that is:
[tex]m\angle A+m\angle D+m\angle E=180[/tex]
solving for angle E, we get
[tex]m\angle E=180-m\angle D-m\angle A[/tex]
Replacing the known values
[tex]\begin{gathered} m\angle E=180-54-67 \\ m\angle E=59 \end{gathered}[/tex]
To find then measure of angle BEC, we need to notice that this angle is equal to angle E, therefore:
[tex]m\angle\text{BEC}=m\angle E=59[/tex]
The measure of angle BEC is 59
