The three angles of a triangle measure 2x – 6, 3x + 5, and 2x + 20. What is the measure of the smallest angle in degrees

Smallest angle = 40

Step-by-step explanation:

Angle sum property:Sum of all three angles of triangle is 180

2x - 6 + 3x + 5 + 2x + 20 = 180   {Combine like terms}

2x + 3x + 2x - 6 + 5 + 20 = 180

                     7x  + 19       = 180            {Subtract 19 from both sides}

                                  7x = 180 - 19

                                  7x = 161               {Divide both sides by 7}

                                    x = 161/7

x = 23

2x - 6 = 2*23 - 6 = 46 - 6 = 40

3x + 5 = 3*23 + 5 = 69 + 5 = 74

2x + 20 = 2*23 + 20 = 46 + 20 = 66

Smallest angle = 40

so a parallelogram is just like a square base times height. multiply 40 and 39 to get 1560 inches.

a triangle is base times height divided by two. so multiply 7.9 and 5 and then divide it by 2 to get 19.75inches.

the kite can be split into two separate triangles and added together to get the total area. 30 x 4 /2 which equals 60. make sure to double it for the two triangles making 120.

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)