Respuesta :
Answer:
The value of x is 41.19
Step-by-step explanation:
Given as for a regular polygon :
The angles of polygon are as
120° , (3x+5)° , x° , 45° , 135° , (x-45) , 5x°
∵ The numbers of angles of polygon are 7 ,
∴ The sides of polygon are 7
Now, each internal angle of regular polygon is with n sides
180° - [tex]\frac{360}{n}[/tex]
So, Let (3x+5)° = 180° - [tex]\frac{360}{n}[/tex]
or, (3x+5)° = 180° - [tex]\frac{360}{7}[/tex]
Or, (3x+5)° = 180° - 51.42°
Or, (3x+5)° = 128.58°
Or, 3x = 128.58° - 5° = 123.58°
∴ x = [tex]\frac{123.58}{3}[/tex] = 41.19
Hence The value of x is 41.19 Answer
The sum of the internal angle of the heptagon is 900. Then the value of x is 64 degrees.
What is a polygon?
It is a polygon that has n sides. The sum of the internal angle is given as,
[tex]n(180 - \dfrac{360}{n})[/tex] where n is the number of sides.
The angles of a regular polygon are 120, (3x+5), (x), 45, 135, (x-45), and (5x) degrees.
Then the sum will be
[tex]\begin{aligned} 120 + 3x+ 5 +x +45+135+x-45+5x &=n(180 - \dfrac{360}{n})\\\\10x +260 &= n(180 - \dfrac{360}{n})\end{aligned}[/tex]
The number of sides is equal to the number of angles.
Then n = 7
[tex]\begin{aligned} 10x +260 &= 7(180 - \dfrac{360}{7})\\\\10x +260 &= 7*128.57\\\\10x + 260 &= 900 \\\\10x &= 900 - 260\\\\x &= \dfrac{640}{10}\\\\x &= 64\end{aligned}[/tex]
Thus, the value of x is 64 degrees.
More about the polygon link is given below.
https://brainly.com/question/17756657
