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°

Step-by-step 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°