Question

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

Answer 1

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

`\therefore(3x-4)=59`

Now let us solve the equation to find x

→ Add 4 to both sides

`\begin{gathered} \because3x-4+4=59+4 \\ \therefore3x+0=63 \\ \therefore3x=63 \end{gathered}`

→ Divide both sides by 3 to find x

`\begin{gathered} \because(3x)/(3)=(63)/(3) \\ \therefore x=21 \end{gathered}`

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

`\therefore2y=59`

→ Divide both sides by 2 to find y

`\begin{gathered} \because(2y)/(2)=(59)/(2) \\ \therefore y=29.5 \end{gathered}`

∴ x = 21 and y = 29.5