In a set of three lines, a pair of parallel lines is intersected by a transversal. the intersection forms eight special angles. two of the special angles, ∠a and ∠b, are corresponding angles.
for the set of parallel lines intersected by a transversal, a = 4x and b = 2(x+14).

use an equation to represent the corresponding angle relationship between a and b.
use the equation to find the measures of a and b.

Use an equation to represent the corresponding angle relationship between A and B.

Ans:

4x = 2(x + 14)

Since they are corresponding, they are considered equal.

Use the equation to find the measures of A and B.

Ans: Solve for x and substitute it for the angles.

4x = 2(x + 14)

4x = 2x + 28

4x - 2x = 28

2x = 28

x = 28 ÷ 2

x = 14

Now substitute:

Remember, ∠A = ∠B

∠A = 4(14)

∠B = 2(14 + 14)

4(14) = 2(14 + 14)

56 = 2(28)

56 = 56

Correct

56° is the measure for angles for ∠A and ∠B

answer is 8x+24

area of vanessa's patio = length × width

given, length = (3x² + 5x + 10)

width = (x² - 3x - 1)

area of vanessa's patio = (3x² + 5x + 10)(x² - 3x - 1)

= 3x²(x² - 3x - 1) + 5x(x² - 3x - 1) + 10(x² - 3x - 1)

= 3x⁴ - 9x³ - 3x² + 5x³ - 15x² - 5x + 10x² - 30x - 10

= 3x⁴ - 4x³ - 8x² - 35x - 10

hence, expression of vanessa's patio = (3x⁴ - 4x³ - 8x² - 35x - 10)

answer: apothems is your answer

step-by-step explanation: hope u get it right