Statements a, c, d, and e are true. Only b is false.
Statement a: FGD is an exterior angle of triangle DHG.
True.
An exterior angle of a triangle is formed by one side of the triangle and a non-adjacent side extended. In this diagram, FGD is formed by side DG extended and side FG.
Statement b: m∠EFD+m∠HGD=m∠FDG
False.
The measure of the exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles. In this diagram, the remote interior angles are ∠EFD and ∠HGD. Therefore, the correct statement is:
m∠FDG = m∠EFD + m∠HGD
Statement c: m∠DFH+m∠FDH=m∠GHM
True.
Angles DFH and FDH are supplementary angles, meaning that their measures add up to 180 degrees. Therefore, the correct statement is:
m∠DFH + m∠FDH = 180 degrees
Statement d: m/GD4+m/D4G=m/FGI
True.
Angles GD4 and D4G are vertical angles, meaning that they are equal in measure. Therefore, the correct statement is:
m/GD4 + m/D4G = m/FGI
Statement e: m∠DHJ+m∠DGE+m∠BDH=360 degrees
True.
The sum of the measures of the angles in a triangle is always 180 degrees. In this diagram, triangle DHJ has angles ∠DHJ, ∠DGE, and ∠BDH. Therefore, the correct statement is:
m∠DHJ + m∠DGE + m∠BDH = 180 degrees