Question

Find the value of x and y if DEFG is congruent to SPQR

Answer 1

• x = 8

,

• y = 10

Step-by-step explanation

If DEFG is congruent to SPQR, then side QR is congruent to side FG,

`2x-4=12`

Add 4 to both sides of the equation,

`\begin{gathered} 2x-4+4=12+4 \\ 2x=16 \end{gathered}`

And divide both sides by 2,

`\begin{gathered} (2x)/(2)=(16)/(2) \\ x=8 \end{gathered}`

For the same reason, angles F and Q are congruent,

`6y+x=68`

Replace x by the value we found before,

`6y+8=68`

Subtract 8 from both sides of the equation,

`\begin{gathered} 6y+8-8=68-8 \\ 6y=60 \end{gathered}`

And divide both sides by 6,

`\begin{gathered} (6y)/(6)=(60)/(6) \\ y=10 \end{gathered}`

Hence, the answers are x = 8 and y = 10.