NEED ASAP 50 POINTS!! In the following diagram line C intersects line D. 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.

∠7 and ∠8 are vertically opposite angles. Since lines C and D are straight lines and intersect each other, ∠7 and ∠8 are equal and angle (5y-29) equal to angle (3y+19). y = 24, ∠7 = 89° and ∠8 = 89°.

Step-by-step explanation:

Vertically opposite angles are angles that are directly opposite each other when two straight lines intersect each other and create an "X". Now that you know (5y-29) = (3y+19), you can solve for y like this:

5y-29 = 3y+19

5y-3y = 19+29 (Keep the like terms on one side)

2y = 48 (Simplify)

y = 48÷2 (Further simplify)

y = 24

To find ∠7, you must remember that 5y-29+∠7 = 180° since they are on the same line. The same goes for 3y+19 and ∠8.

∠7 = 180°-(5×24)+29

     = 89°

∠8 = 180°-(3×24)-19

     = 89°

∠7 and ∠8 both equals to 89° so it is confirmed that they are vertically opposite angles.

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