Question

Please help with #8 refer to the other answers one as a guide

Answer 1

Given:

`\begin{gathered} m\angle2=2x-5 \\ \\ m\angle\text{FDE}=3x-1 \end{gathered}`

As PD is a angle bisector, the measure of angle 2 is the half of the measure of angle FDE:

`\begin{gathered} m\angle2=(1)/(2)m\angle FDE \\ \\ 2x-5=(1)/(2)(3x-1) \end{gathered}`

Use the equation above to solve x:

`\begin{gathered} 2x-5=(3)/(2)x-(1)/(2) \\ \\ 2x-(3)/(2)x-5=(3)/(2)x-(3)/(2)x-(1)/(2) \\ \\ 2x-(3)/(2)x-5+5=-(1)/(2)+5 \\ \\ 2x-(3)/(2)x=-(1)/(2)+5 \\ \\ (4)/(2)x-(3)/(2)x=-(1)/(2)+(10)/(2) \\ \\ (1)/(2)x=(9)/(2) \\ \\ (2)((1)/(2)x)=(2)((9)/(2)) \\ \\ x=9 \end{gathered}`

Then, the value of x is 9