The complete sentences are:
- The relationship between angles 7 and 8 is that they are vertical opposite angles
- The special angles created by the intersection of lines C and D are vertically opposite angles and adjacent angles
- The value of y is 24, and the measure of angles 7 and 8 is 89 degrees
Relationship between <7 and <8
From the attached figure, we can see that:
- Lines C and D intersect at a point
- There are 4 angles at the point of intersection of lines C and D
- Angles 7 and 8 are vertical and are also at opposite sides
The above highlights mean that:
Angle 7 and 8 are vertically opposite angles
Special angles created by lines C and D
Using the highlights in (a) above, the special angles created are:
- Vertically opposite angles
- Adjacent angles
Value of y, and the measures of <7 and <8
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 value of y is 24, and the measure of angles 7 and 8 is 89 degrees
Read more about intersecting lines at:
https://brainly.com/question/14362353
