Question
What is the value of x in the regular polygon below?
A regular hexagon is shown with one angle labeled 3 x degree-sign.
(1 point)
Responses
40
40
120
120
60
60
150
The value of x in the regular polygon is 40 degrees.
To find the value of x in the regular hexagon, we can use the fact that the sum of the angles in a polygon can be determined by the formula: (n-2) * 180 degrees, where n is the number of sides in the polygon.
Since a regular hexagon has six sides, we can substitute n=6 into the formula: (6-2) * 180 degrees = 4 * 180 degrees = 720 degrees.
Now, we can find the measure of each angle in the regular hexagon by dividing the sum of the angles by the number of sides: 720 degrees / 6 sides = 120 degrees.
Therefore, the value of x is 120 degrees.
To find the value of x in the regular polygon, we need to determine the measure of each angle in the polygon and then solve for x.
In a regular polygon, all angles have the same measure. To find the measure of each angle, we use the formula:
Sum of interior angles = (n - 2) * 180 degrees
where n is the number of sides in the polygon.
For a hexagon (a polygon with six sides), the formula becomes:
Sum of interior angles = (6 - 2) * 180 degrees = 4 * 180 degrees = 720 degrees
Since a regular hexagon has six equal angles, we can divide the sum of interior angles (720 degrees) by the number of angles (6) to find the measure of each angle:
Measure of each angle = 720 degrees / 6 = 120 degrees
Now that we know the measure of each angle in the regular hexagon is 120 degrees, we can solve for x. According to the question, one angle is labeled as 3x degrees. Therefore, we can set up the following equation:
3x = 120 degrees
To solve for x, we divide both sides of the equation by 3:
3x / 3 = 120 degrees / 3
x = 40 degrees
Therefore, the value of x in the regular polygon is 40 degrees.