Find the missing angle measures

Thank you!!

SEE BELOW

Step-by-step explanation:

INTERRIOR ANGLES

3.

∠A + ∠B + ∠C = 180

(180 - 103) + (3x - 14) + (3x + 9) = 180

6x = 180 - 77 + 14 - 9

x = 108 / 6

x = 18

m∠ACB = (3x - 14)

             = 3(18) - 14

             = 40

m∠ABC = (3x + 9)

              = 3(18) + 9

              = 63

INTERRIOR ANGLES

4.

∠A + ∠B + ∠C = 180

(180 - 97) + (2x + 2) + (14x - 1) = 180

16x = 180 - 83 - 2 + 1

x = 96 / 16

x = 6

m∠BCA = 2x + 2

             = 2(6) + 2

             = 14

m∠ABC = 14x - 1

             = 14(6) - 1

             = 83

EXTERIOR ANGLES

5.

∠B

180 - 15x + 20

15x = 180 + 20

   x = 200/15

   x = 13.33

∠C

180 - 9x + 10  

9x = 190

 x = 190/9

 x = 21.11

∠E

180 - 17x + 2

17x = 182

  x = 182/17

  x = 10.706

m∠BEF = 17x + 2

             = 17 (10.706) + 2

             = 184

m∠ABC = 15x + 20

             = 15(15.33) + 20

             = 220

EXTERIOR ANGLES

6.

first solve x by adding all the interior angles = 180

∠B + ∠E + ∠C = 180

2x + x + 93 = 180

3x = 180 - 93

x = 87/2

x = 43.5

m∠BEC = 360 - x

             = 360 - 43.5

             = 316.5

m∠ABC = 180 - 2x

             = 180 - 2(43.5)

             = 93

b.an increase in a causes b to decrease

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240