In the figure below, BE and CF intersect at point A. Points G and D are in the interiors of angles
∠BAF and ∠CAE, respectively. Some angle measures are given. What is the measure of ∠BAG ?
Approach
∠CAD, ∠DAE, and ∠EAF should add up to 180∘ since they make up all the angles along the bottom portion of line CF.
56∘+m∠DAE+64∘=180∘m∠DAE=60∘
∠BAC≅∠EAF since they are vertical angles (opposite of each other where lines cross).
We can then sum up all of the angles to 360∘. Starting at ∠BAG and going clockwise: