ANSWER
• x = 8
,
• y = 10
EXPLANATION
If DEFG is congruent to SPQR, then side QR is congruent to side FG,
[tex]2x-4=12[/tex]
Add 4 to both sides of the equation,
[tex]\begin{gathered} 2x-4+4=12+4 \\ 2x=16 \end{gathered}[/tex]
And divide both sides by 2,
[tex]\begin{gathered} \frac{2x}{2}=\frac{16}{2} \\ x=8 \end{gathered}[/tex]
For the same reason, angles F and Q are congruent,
[tex]6y+x=68[/tex]
Replace x by the value we found before,
[tex]6y+8=68[/tex]
Subtract 8 from both sides of the equation,
[tex]\begin{gathered} 6y+8-8=68-8 \\ 6y=60 \end{gathered}[/tex]
And divide both sides by 6,
[tex]\begin{gathered} \frac{6y}{6}=\frac{60}{6} \\ y=10 \end{gathered}[/tex]
Hence, the answers are x = 8 and y = 10.
