What is the value of x in the regular polygon below?
3 * x deg
(1 point)
A.40
B. 120
C.60
D.150
Since a regular polygon has all its angles equal, then the value of x can be determined by dividing 360 (the sum of all the angles in a polygon) by the number of sides in the polygon.
The formula is:
x = 360 / number of sides
However, the number of sides of the polygon is not given in the question, so it is impossible to determine the exact value of x without that information.
To find the value of x in the regular polygon, we need to use the formula for the interior angles of a regular polygon, which is:
Interior Angle = (n-2) * 180 / n
where n is the number of sides of the polygon.
In this case, the formula becomes:
3 * x = (3-2) * 180 / 3
Simplifying further:
3 * x = 1 * 180 / 3
3 * x = 180 / 3
Dividing both sides by 3:
x = 60 / 3
x = 20
Therefore, the value of x in the regular polygon is 20 degrees.
The correct answer is:
C. 60
There is 6 sides
Apologies for the misunderstanding.
If the regular polygon has 6 sides, we can use the formula:
Interior Angle = (n-2) * 180 / n
where n is the number of sides of the polygon.
Plugging in the values:
3 * x = (6 - 2) * 180 / 6
3 * x = 4 * 180 / 6
3 * x = 720 / 6
3 * x = 120
Dividing both sides by 3:
x = 120 / 3
x = 40
Therefore, the value of x in the regular polygon with 6 sides is 40 degrees.
The correct answer is:
A. 40
To find the value of x in the given regular polygon, we need to apply the formula:
Sum of interior angles of a polygon = (n - 2) * 180 degrees
where n is the number of sides of the polygon.
Since the given regular polygon has 3 * x degrees as one of its interior angles, we can set up the equation as follows:
3 * x = (n - 2) * 180
By comparing the options provided, we can substitute the values for x to see if they satisfy the equation.
Let's start with option A: x = 40 degrees.
Substituting x = 40 into the equation:
3 * 40 = (n - 2) * 180
120 = (n - 2) * 180
120 cannot be achieved by multiplying (n - 2) by any integer value of 180. Hence, option A is incorrect.
Let's move on to option B: x = 120 degrees.
Substituting x = 120 into the equation:
3 * 120 = (n - 2) * 180
360 = (n - 2) * 180
By dividing both sides of the equation by 180:
360 / 180 = n - 2
2 = n - 2
Since 2 = n - 2, n must be 4.
Thus, option B is correct. The value of x in the regular polygon is 120 degrees.
Therefore, the answer is B.