(HELP ME ASAP PLEASE) In the following diagram, A || B.
Use complete sentences to explain how the special angles created by the intersection of A and B by D can be used to solve for x.
Solve for x, showing all of your work.
Find the measure of ∠6.

In the following diagram line C intersects line D.

Figure may not be drawn to scale.

Using complete sentences, classify the relationship between ∠7 and ∠8 created by the intersection of lines C and D.
Use complete sentences to explain how the special angles created by the intersection of lines C and D can be used to solve for y.
Solve for y and find the measures of ∠7 and ∠8

Angles 7 and 8 are vertical opposite angles
The special angles created are vertically opposite angles and adjacent angles
The value of y is 24, and the measure of angles 7 and 8 is 89 degrees

From the attached figure, we can see that:

The point of intersection of lines C and D created 4 angles
A pair of angles are either vertically opposite angles or adjacent angles

Using the second highlight above, we have:

[tex]\angle 7 \cong \angle 8[/tex]

The above means that:

Angle 7 and 8 are congruent

The congruence relationship between both angles is vertically opposite angles

Using the second highlight above, we have:

[tex]\angle 7 \cong \angle 8[/tex]

[tex]\angle 7 + 5y - 29 = 180[/tex]

This means that, the special angles created are:

We have:

[tex]5y - 29 = 3y + 19[/tex] --- vertically opposite angles

Collect like terms

[tex]5y - 3y = 29 + 19[/tex]

[tex]2y = 48[/tex]

Divide both sides by 2

[tex]y = 24[/tex]

To calculate <7, we have:

[tex]\angle 7 + 5y - 29 = 180[/tex] ---- adjacent angles

Substitute 24 for y

[tex]\angle 7 + 5\times 24 - 29 = 180[/tex]

[tex]\angle 7 + 120- 29 = 180[/tex]

[tex]\angle 7 + 91 = 180[/tex]

Subtract 91 from both sides

[tex]\angle 7 = 89[/tex]

Hence, the measure of angles 7 and 8 is 89 degrees

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