Respuesta :

Poltergeist

Answer:

[tex]x=9[/tex]

Step-by-step explanation:

The expression is for the interior angle of the hexagon; one interior angle is equal to [tex](11x+21)^o[/tex].

Since an interior angle of a hexagon measures 120°, we have the equality

[tex](11x+21)=120[/tex].

Now it is just a matter of solving for [tex]x:[/tex]

[tex]11x=120-21\\\\11x=99\\\\x=\frac{99}{11} \\\\\boxed{x=9}[/tex]

rahulsharma789888

The value of x for regular hexagon is 9

A polygon is called as a regular polygon when all the angles of the polygon are equal and all the sides of the polygon are equal.

The sum of interior angles of a regular polygon is given by the formula

[tex]\rm S = (n-2)180\textdegree,,,,,,,,,,(1) \\where \; n \;is \;the\; number\; of \; sides \; of \; the\; regular\; polygon \\\\S= Sum \; of \; the \; interior\; angles[/tex]

For a hexagon  n = 6

hence on putting n = 6 in equation (1) we get

[tex]\rm S = (6-2) 180\textdegree = 720\textdegree[/tex]

So the sum of interior angles  for a hexagon = 720°

So the measure of one angle of hexagon =  720°/6 = 120°

According to the condition given in the question

Measure of one angle = (11x+21)°

[tex]\rm 11x +21 = 120[/tex]

[tex]\rm 11x = 120-21\\11x = 99\\x = 99/11 = 9 \\x =9[/tex]

So the value of x for regular hexagon is 9

For more information please refer to the link given below

https://brainly.com/question/19023938

Otras preguntas