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how do i find the value of x and y in geomatry

Sagot :

From the given figure

∵ There are 2 parallel lines intersected by another line called a transversal

∴ The angles of measures 59 degrees and (3x - 4) degrees are

corresponding angles

∵ Corresponding angles are equal in measures

[tex]\therefore(3x-4)=59[/tex]

Now let us solve the equation to find x

→ Add 4 to both sides

[tex]\begin{gathered} \because3x-4+4=59+4 \\ \therefore3x+0=63 \\ \therefore3x=63 \end{gathered}[/tex]

→ Divide both sides by 3 to find x

[tex]\begin{gathered} \because\frac{3x}{3}=\frac{63}{3} \\ \therefore x=21 \end{gathered}[/tex]

Now let us find y

∵ The angles of measures 59 degrees and (2y) degrees are

vertically opposite angles

∵ The vertically opposite angles are equal in measures

[tex]\therefore2y=59[/tex]

→ Divide both sides by 2 to find y

[tex]\begin{gathered} \because\frac{2y}{2}=\frac{59}{2} \\ \therefore y=29.5 \end{gathered}[/tex]

∴ x = 21 and y = 29.5

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