Answer:
x = 7.5 , ∠ EGB = 75° , ∠ EGA = 105°
Step-by-step explanation:
∠ CHF and ∠ EGB are alternate exterior angles and are congruent (equal), so
10x = 2x + 60 ( subtract 2x from both sides )
8x = 60 ( divide both sides by 8 )
x = 7.5
substitute x = 7.5 into ∠ EGB
∠ EGB = 2x + 60 = 2(7.5) + 60 = 15 + 60 = 75°
∠ EGA and ∠ EGB are a linear pair and sum to 180° , that is
∠ EGA + ∠ EGB = 180° ( substitute values )
∠ EGA + 75° = 180° ( subtract 75° from both sides )
∠ EGA = 105°
