Question

In the following diagram line C Intersects line D.ABDSy-2928272425 4x+53y+19262221233x+7Figure may not be drawn to scale.A. Using complete sentences, classify the relationship between 27 and 28 created by the Intersection of lines C andD.B. Use complete sentences to explain how the special angles created by the Intersection of lines C and D can be usedto solve for y.C. Solve for y and find the measures of 27 and 28.

Answer 1

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.

Step-by-step 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.

`5y-29=3y+19`

By solving the above equation we can find the value of y.

(c)

`5y-29=3y+19`

Subtract 3y on both sides.

`\begin{gathered} 5y-29=3y+19 \\ 5y-29-3y=3y+19-3y \\ 2y-29=19 \end{gathered}`

Add 29 on both sides.

`\begin{gathered} 2y-29+29=19+29 \\ 2y=48 \\ y=(48)/(2) \\ y=24 \end{gathered}`

We know that the sum of linear angles is 180 degrees.

`5y-29+\angle7=180\degree`

Substitute the value of y.

`\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}`
`3y+19+\angle8=180\degree`

Substitute the value of y.

`\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}`

Final Answer:

(a) Angle 7 and angle 8 are vertically opposite angles.

(b)

`5y-29=3y+19`

(c)

`\begin{gathered} y=24\degree \\ \angle7=\angle8=89\degree \end{gathered}`