Given:
Line C intersects line D in the given figure.
Required:
(a) Classify the relation between angle 7 and angle 8.
(b) Explain the angles created by the intersection of lines C and D to solve for y.
(c) Solve for y and find the measure of angles 7 and 8.
Explanation:
(a) The lines C and D intersect each other so the angles 7 and 8 will be equal by the property of vertically opposite angles.
(b) Since vertically opposite angles are equal so angles 5y-29 and 3y+19 will be equal.
[tex]5y-29=3y+19[/tex]By solving the above equation we can find the value of y.
(c)
[tex]5y-29=3y+19[/tex]Subtract 3y on both sides.
[tex]\begin{gathered} 5y-29=3y+19 \\ 5y-29-3y=3y+19-3y \\ 2y-29=19 \end{gathered}[/tex]Add 29 on both sides.
[tex]\begin{gathered} 2y-29+29=19+29 \\ 2y=48 \\ y=\frac{48}{2} \\ y=24 \end{gathered}[/tex]We know that the sum of linear angles is 180 degrees.
[tex]5y-29+\angle7=180\degree[/tex]Substitute the value of y.
[tex]\begin{gathered} 5(24)-29+\angle7=180\degree \\ 120-29+\angle7=180\degree \\ 91+\angle7=180\degree \\ \angle7=180\degree-91 \\ \angle7=89\degree \end{gathered}[/tex][tex]3y+19+\angle8=180\degree[/tex]Substitute the value of y.
[tex]\begin{gathered} 3(24)+19+\angle8=180\degree \\ 72+19+\angle8=180\degree \\ 91+\angle8=180\degree \\ \angle8=180\degree-91 \\ \angle8=89\degree \end{gathered}[/tex]Final Answer:
(a) Angle 7 and angle 8 are vertically opposite angles.
(b)
[tex]5y-29=3y+19[/tex](c)
[tex]\begin{gathered} y=24\degree \\ \angle7=\angle8=89\degree \end{gathered}[/tex]