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
.

The answer is 7^2

Step-by-step explanation:

They are congruent in accordance with the opposite angles theorem, which states that when two lines cross, four angles are created and the opposite angles are equal.  

Since both pairs of angles are congruent it follows that 5y - 29 is equal to 3y + 19. By resolving this equation, y can be found to be 24. Both angles therefore equal 91 degrees.

The value of angle 7 is the supplement of one of the angles containing y described above and equals 89 degrees. The value of angle 8 as previously shown is also 89 degrees.

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