Question

each area of a regular polygon measures 45 degrees etc.......

Answer 1

Answers

1) part I:         8 sides

 Name:        Octagon

 Part II: 1,080

2) part I:   17

   part II: m<A = 86°

               m<D = 94°

Explanation

Q1) part 1

In a regular polygon,

The sum of exterior angle = 360

let n be the number of sides

∴ 45n = 360

  n = 8 sides

Name: Octagon

part 2

exterior angle + interior angle = 180

Interior angle = 180 - 45°

                      = 135°.

Sum of interior angles = 8 × 135

                                       = 1,080°

Q2

Part I:

The opposite sides of a paralellogram are equal

5x + 2 = 8x - 7

5x - 8x = -7 - 2

  - 3x = - 9

x = 3

AB = CD = 5(3) + 2

                = 15+2

                 = 17

Part II

2y + 50 + 3y + 40 = 180

5y + 90 = 180

5y = 180 - 90

       = 90

y = 90/5

     = 18

Angle A = 2y + 50

              = 2(18) +50

             = 86°

Angle D = 3y + 40

              = 3(18) + 40

                =54 + 40

                  = 94°