Question

Given AD || BC, m Z A = 67, andmZD=54Find mZBEC

Answer 1

we are given the following measurements for two angles of a triangle

`\begin{gathered} m\angle A=67 \\ m\angle D=54 \end{gathered}`

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:

`m\angle A+m\angle D+m\angle E=180`

solving for angle E, we get

`m\angle E=180-m\angle D-m\angle A`

Replacing the known values

`\begin{gathered} m\angle E=180-54-67 \\ m\angle E=59 \end{gathered}`

To find then measure of angle BEC, we need to notice that this angle is equal to angle E, therefore:

`m\angle\text{BEC}=m\angle E=59`

The measure of angle BEC is 59