Find the sum of the measures of the interior angles of each of the following convex polygons: a pentagon, an octagon, a dodecagon, a forty-sided polygon, a fifty-two sided polygon, a hundred sided polygon.

pentagon=540°

octagon= 1080°

decagon= = 1440°

forty-sided polygon= 6840°

fifty-two-sided polygon=9000°

hundred-sided polygon=17640°

Step-by-step explanation:

To find the measure of the sum of the interior angle of a polygon, we will simple use the formula;

sum of interior angle = (n-2)180

where n is the number of sides of the polygon

We are ask to find the sum of the interior angle of a pentagon, octagon, decagon, a forty-sided polygon, a fifty-two-sided polygon and a hundred-sided polygon.

First we need to define some terminology;

A penatgon is a five(5)-sided polygon

An Octagon is an eight(8)-sided polygon

A Decagon is a ten(10)-sided polygon

We can now proceed to solve

sum of interior angle = (n-2)180

Sum of interior angle of a pentagon = (5-2)180

                                                             = 3 × 180

                                                             =540°

Sum of interior angle of a pentagon = 540°

Sum of interior angle of an octagon  = (8-2)180

                                                             = 6 × 180

                                                             =1080°

Sum of interior angle of an octagon = 1080°

Sum of interior angle of a decagon  = (10-2)180

                                                             = 8 × 180

                                                             =1440°

Sum of interior angle of a decagon = 1440°

Sum of interior angle of a forty-sided polygon  = (40-2)180

                                                                               = 38 × 180

                                                                                =6840°

Sum of interior angle of a forty-sided polygon = 6840°

Sum of interior angle of a fifty-two-sided polygon  = (52-2)180

                                                                                    = 50 × 180

                                                                                     =9000°

Sum of interior angle of a fifty-two-sided polygon = 9000°

Sum of interior angle of a hundred-sided polygon  = (100-2)180

                                                                                     = 98 × 180

                                                                                      =17640°

Sum of interior angle of a hundred-sided polygon = 17640°

1/4 and 8/3 because:

the reciprocal if 4 is 1/4 because 4 is used as 4/1 and the opposite of that is 1/4. the opposite of 3/8 is 8/3 so that is the answer.

(x3 + 6x2 + 2x - 6) • (x - 1)

step-by-step explanation:

polynomial long division :

3.2     polynomial long division

dividing :   x4+5x3-4x2-8x+6

                              ("dividend")

by         :     x-1     ("divisor")

dividend     x4   +   5x3   -   4x2   -   8x   +   6

- divisor   * x3     x4   -   x3            

remainder         6x3   -   4x2   -   8x   +   6

- divisor   * 6x2         6x3   -   6x2        

remainder             2x2   -   8x   +   6

- divisor   * 2x1             2x2   -   2x    

remainder               -   6x   +   6

- divisor   * -6x0               -   6x   +   6

remainder                     0

quotient :   x3+6x2+2x-6   remainder:   0