Respuesta :
Answer:
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°
The sum of the measure of the interior angles of each of the following convex polygons with hundred sided polygon is 17,640°.
What is the sum of the interior angles of a polygon?
The sum of the interior angles of n sided polygon can be written as       (n-2)180°.
Given to us
- A pentagon,
- An octagon,
- A dodecagon,
- A forty-sided polygon,
- A fifty-two sided polygon,
- A hundred-sided polygon.
We know the sum of the interior angles of n sided polygon can be written as (n-2)180°. therefore,
The sum of the interior angles of a pentagon
We know that a pentagon has 5 number of sides, therefore, the value of n is 5.
The sum of the interior angles of a pentagon = (n-2)180°
                                      = (5-2)180°
                                      = 540°
The sum of the interior angles of an Octagon
We know that an octagon has 8 sides, therefore, the value of n is 8.
The sum of the interior angles of an octagon = (n-2)180°
                                     = (8-2)180°
                                     = 1,080°
The sum of the interior angles of a dodecagon
We know that a dodecagon has 12 sides, therefore, the value of n is 12.
The sum of the interior angles of a dodecagon = (n-2)180°
                                        = (12-2)180°
                                        = 1,800°
The sum of the interior angles of a forty-sided polygon
The sum of the interior angles of a forty-sided polygon = (n-2)180°
                                              = (40-2)180°
                                              = 6,840°
The sum of the interior angles of a fifty-sided polygon
The sum of the interior angles of a fifty-sided polygon = (n-2)180°
                                             = (52-2)180°
                                             = 9,000°
The sum of the interior angles of a hundred-sided polygon
The sum of the interior angles of a hundred-sided polygon = (n-2)180°
                                                 = (100-2)180°
                                                 = 17,640°
Hence, the sum of the measure of the interior angles of each of the following convex polygons with hundred sided polygon is 17,640°.
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