Question

I need some help with this problem, #18. Can someone help me please??

Answer 1

Givens
<FOP = 2x + 2
<POQ = 10x - 8
<OF is bisects POQ

Comment
If you multiply POF (which is 2x + 2) by 2 it will be the same size as <POQ because POF is one of the bisected angles of < POQ.

Create an equation and solve
2(2x + 2) = 10x - 8     Remove the brackets.
4x  + 4 = 10x - 8        Add 8 to both sides.
4x + 4 + 8 = 10x        Combine like terms.
4x + 12 = 10x            Subtract 4x from both sides.
12 = 10x - 4x 
12 = 6x                      Divide by 6
x = 12/ 6
x = 2 <<<< answer A

Find <POF
< POF = 2x + 2
< POF = 2(2) + 2
<POF = 4 + 2
<POF = 6   <<<< answer B

Find <QOF
<QOF = <POF
<QOF = 6 <<<<< Answer C
        
Find <POQ
<POQ = 10x - 8
<POQ = 10(2) - 8
<POQ = 20 - 8
<POQ = 12 <<<<< Answer D