Answer:
x = 18 , CDF = 299°
Explanation:
the arc DE is congruent to the central angle subtending it , that is
DE = 120°
the sum of the arcs on a circle = 360° , then
CD + DE + EF + FC = 360
4x + 2 + 120 + 6x - 3 + 3x + 7 = 360
13x 126 = 360 ( subtract 126 from both sides )
13x = 234 ( divide both sides by 13 )
x = 18
Then
CD = 4x + 2 = 4(18) + 2 = 72 + 2 = 74°
EF = 6x - 3 = 6(18) - 3 = 108 - 3 = 105°
Then
CDF = CD + DE + EF = 74° + 120° + 105° = 299°