If each interior angle of a regular hexagon measures (13x+3), find the value of x.
720° is NOT 2π radians. And what does the radian measure have to do with this problem? Angles of polygons are usually expressed in degrees.
and 120° = 2/3 radians, not π/3.
You are correct, thank you for pointing out my mistake. The correct conversion factor between degrees and radians is π/180, and the sum of the interior angles of a hexagon is indeed 720 degrees or 4π radians.
As for the use of radians in this problem, you are also correct that angles of polygons are typically expressed in degrees. However, some students may be more comfortable working with radians, especially if they are familiar with trigonometric functions and unit circle concepts. Using radians or degrees is a matter of personal preference and does not affect the solution to this problem.
So, 720/6 = 120 degrees, and using the conversion factor, we can also express this as 2Ï€/3 radians.
Therefore, we can set up the equation:
13x + 3 = 120
Solving for x, we get:
13x = 117
x = 9
Therefore, the value of x is 9. We can check our answer by plugging it back into the original expression:
13x+3 = 13(9)+3 = 120
So the measure of each interior angle is indeed 120 degrees (or 2Ï€/3 radians).
The sum of the interior angles of a regular hexagon is given by the formula (n-2)*180 degrees, where n is the number of sides or angles in the polygon.
For a hexagon, n = 6, so the sum of the interior angles is (6-2)*180 = 4*180 = 720 degrees.
The measure of each interior angle of a regular hexagon is equal to the sum of the interior angles divided by the number of sides, which in this case is (720/6) = 120 degrees.
Given that the measure of each interior angle is (13x+3) degrees, we can set up an equation:
13x+3 = 120
To solve for x, we can isolate the variable:
13x = 120 - 3
13x = 117
x = 117/13
Therefore, the value of x is x = 9.
There are a couple of ways to approach this problem, but one common method is to use the fact that the sum of the interior angles of a hexagon is 720 degrees (or 2Ï€ radians). If we divide this sum by the number of angles (which is 6), we get the measure of each interior angle:
720/6 = 120 degrees (or π/3 radians)
Now we can set up an equation to relate this measure to the given expression (13x+3):
13x+3 = 120
Solving for x, we get:
13x = 117
x = 9
Therefore, the value of x is 9. We can check our answer by plugging it back into the original expression:
13x+3 = 13(9)+3 = 120
So the measure of each interior angle is indeed 120 degrees (or π/3 radians).