What is the sum of the measures of the exterior angles of this triangle?

360

Step-by-step explanation:

112 - 51 = 61 (m∠A = 61)

180 - 61 = 119 (m∠B = 119)

180 - 51 = 129

119 + 112 + 129 = 360

Step-by-step explanation:

∠AEB + ∠FEC = 180   {linear pair}

∠AEB = 180 - 4x

DE // AB , AE is transversal,

∠EAB = ∠DEA   {Alternate interior angles}

∠EAB = 2x

∠EBC = ∠AEB + ∠EAB  {Exterior angle property}

    6x  =  180 - 4x + 2x

    6x = 180 - 2x

Add 2x to both sides

6x + 2x = 180

8x = 180

x = 180/8

x = 22.5