Answer
x = 17
Step-by-step Explanation
The question gives us Angle DEF as (3x + 1) and Angle DEG as (5x + 19).
Note that G is the lower end of the diagram.
What isn't evident from the diagram is that Line EF is a bisector for the DEG.
If Line EF is the bisector, this means that it divides the angle into two equal parts.
(Angle DEG) = (Angle DEF) + (Angle FEG)
Angle DEG = (5x + 19)
Angle DEF = (3x + 1)
Angle FEG = Angle DEF (Since we already established that line EF being a bisector means it divides Angle DEG into two equal parts)
So,
Angle FEG = Angle DEF = (3x + 1)
(Angle DEG) = (Angle DEF) + (Angle FEG)
Substituting the parameters
(5x + 19) = (3x + 1) + (3x + 1)
5x + 19 = 3x + 3x + 1 + 1
5x + 19 = 6x + 2
Collecting like terms by bringing all the coefficients of x to the same side
6x + 2 = 5x + 19
6x - 5x = 19 - 2
x = 17
Hope this Helps!!!
