Respuesta :

The sum of the measures of the angles of a polygon is given by (n - 2)(180), where n is the number of sides.  In this case we would have (9-2)(180)=7(180)=1260.  This is the sum of the angles.  Since it is a regular nonagon, that means that all sides are congruent and all angles are congruent.  Therefore we find the measure of each individual angle by dividing the sum, 1260, by the number of sides, 9.  1260/9=140.  x forms a linear pair with one of the interior angles; that means that the interior angle, 140, added to x would give us 180.  Therefore we find x by subtracting 180-140. x = 40.

The measure of angle x is 40 degrees and this can be determined by using the formula of the sum of interior angles of a polygon.

Given :

A regular nonagon.

The sum of interior angles of a polygon is given by the equation:

= (n - 2)180   --- (1)

where 'n' is the total number of sides of the polygon.

Given that the polygon is the regular nonagon that means the total number of sides is 9.

Now, substitute the value of 'n' in the equation (1).

= (9 - 2)180

= [tex]1260^\circ[/tex]

Now, divide the above expression by 9 in order to get the value of one interior angle.

[tex]= \dfrac{1260}{9}[/tex]

= [tex]140^\circ[/tex]

Now, the sum of one interior angle and the angle x is equal to 180 degrees that means:

140 + x = 180

x = [tex]40^\circ[/tex]

For more information, refer to the link given below:

https://brainly.com/question/19237987

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