Final answer:
The measure of angle BEC is 38°.
Step-by-step explanation:
To find the measure of angle BEC, we need to subtract the given angles mAD and mBC from 180° since BEC is a straight angle.
mBEC = 180° - mAD - mBC
Substituting the given values: mBEC = 180° - 103° - 115° = -38°.
Since angles cannot be negative, we take the positive value of -38° which is 38°.
Therefore, the measure of angle BEC is 38° (option a).