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

Find The Value Of X And Y If DEFG Is Congruent To SPQR class=

Sagot :

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.

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