The Solution.
Step 1:
We shall find two equations from the given angles.
First, by vertically opposite angle property of angles between two lines, we have that:
[tex]\begin{gathered} 7y-23=23x-16 \\ \text{Collecting the like terms , we get} \\ 7y-23x=23-16 \\ 7y-23x=7\ldots.eqn(1) \end{gathered}[/tex]
Similarly, by alternate property of angles between lines, we have that:
[tex]\begin{gathered} 23x-16+8x-21=180 \\ \text{Collecting like terms, we get} \\ 31x-37=180 \\ 31x=180+37 \\ 31x=217 \\ \text{Dividing both sides by 31, we get} \\ x=\frac{217}{31}=7 \end{gathered}[/tex]
Step 2:
We shall find the values of y by substituting 7 for x in eqn(1), we get
[tex]\begin{gathered} 7y-23(7)=7 \\ 7y-161=7 \\ 7y=7+161 \\ 7y=168 \\ \text{Collecting the like terms, we get} \\ y=\frac{168}{7}=24 \end{gathered}[/tex]
Step 3:
Presentation of the Answer.
The correct answers are; x = 7 , and y = 24
