Question

4. If mZDEF = 3x +1 and mZDEG = 5x +19, find the value of x.The image attached isn't the right interpretation of the question.

Answer 1

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!!!