Aregular hexagon is shown below. find the value of x

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

For a hexagon  n = 6

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

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)°

So the value of x for regular hexagon is 9

For more information please refer to the link given below

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Step-by-step explanation:

The expression is for the interior angle of the hexagon; one interior angle is equal to .

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

.

Now it is just a matter of solving for

take the logarithm of both sides (the base of the log doesn't matter):

apply the exponent property - this says that :

distribute the log terms on both sides:

group like terms together:

divide through both sides by the coefficient on :

you can do some additional rewriting here using the properties of the logarithm to simplify things if you like: