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

y = 24

m<7 = 89

m<8 = 89

Step-by-step explanation:

Angles 7 and 8 are nonadjacent angles formed by the intersection of two lines. They are called vertical angles. Vertical angles are congruent, so m<7 = m<8.

Angles 5y - 29 and 3y + 19 are also a pair of vertical angles. They are congruent, so their measures are equal, giving us the following equation:

5y - 29 = 3y + 19

2y =48

y = 24

Now we substitute 24 for y, and we find the measure of angle 3y + 19:

3(24) + 19 = 72 + 19 = 91

m<3y + 19 = 91

Angle 3y + 19 and angle 7 form a linear pair. Angles in a linear pair are supplementary, so their measures add to 180 degrees.

m<7 + (3y + 19) = 180

m<7 + 91 = 180

m<7 = 89

Since angles 7 and 8 are congruent, m<8 = 89.

y = 24

m<7 = 89

m<8 = 89

{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer:   {x = -1/2 ,   y = -1

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