Are the two triangles below similar?
triangles stu and vwx are shown. angle s equals 28 degrees, angle t equals 70 degrees, angle w equals 70 degrees, angle x equals 92 degrees, side st equals 8, side wx equals 4, side vx equals 10.
yes; they have congruent corresponding angles
yes; they have proportional corresponding sides
no; they do not have proportional corresponding sides
no; they do not have congruent corresponding angles

No; they do not have congruent corresponding angles

Step-by-step explanation:

* Lets explain how to solve the problem

* Lets revise the cases of similarity

1) AAA similarity : two triangles are similar if all three angles in the first

  triangle equal the corresponding angle in the second triangle  

2) AA similarity : If two angles of one triangle are equal to the

   corresponding angles of the other triangle, then the two triangles  

   are similar.

3) SSS similarity : If the corresponding sides of two triangles are

   proportional, then the two triangles are similar.

4) SAS similarity : In two triangles, if two sets of corresponding sides  

   are proportional and the included angles are equal then the two  

   triangles are similar.

* Now lets solve the problem

- In ΔSTU

∵ m∠S = 28°

∵ m∠T = 70

∵ The measures of the interior angles of a triangle is 180°

∵ m∠U + m∠T + m∠S = 180°

∴ m∠U + 70° + 28° = 180°

∴ m∠U + 98°  = 180° ⇒ subtract 98° from both sides

∴ m∠U = 82°

- In Δ VWX

∵ m∠W = 70°

∵ m∠X = 92

∵ The measures of the interior angles of a triangle is 180°

∵ m∠V + m∠W + m∠X = 180°

∴ m∠V + 70° + 92° = 180°

∴ m∠V + 162°  = 180° ⇒ subtract 162° from both sides

∴ m∠V = 18°

- In the 2 ΔΔ STU and VWX

∵ m∠S = 28° and m∠V = 18°

∴ m∠S ≠ m∠V

∵ m∠U = 82° and m∠X = 92°

∴ m∠U ≠ m∠X

∴ The corresponding angles not congruent

∴ The two triangles are not similar

* No; they do not have congruent corresponding angles

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)