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

- 2 + 10x³ - 21x² + 19x - 4

step-by-step explanation:

each term in the second factor is multiplied by each term in the first factor

x²(- 2x² + 4x - 1) - 3x(- 2x² + 4x - 1) + 4(- 2x² + 4x - 1) ← distribute

= - 2 + 4x³ - x² + 6x³ - 12x² + 3x -8x² + 16x - 4

collect like terms

= - 2 + 10x³ - 21x² + 19x - 4 ← in standard form