Each exterior angle of a regular decagon has a measure of (3x + 6)°. What is the value of x
To find the value of x, we can use the formula for the sum of the exterior angles of any polygon, which is 360 degrees.
For a decagon (a polygon with 10 sides), the sum of the exterior angles is equal to 360 degrees.
Since each exterior angle of the decagon has a measure of (3x + 6)°, we can set up the equation:
(3x + 6) * 10 = 360
Now, let's solve the equation for x.
30x + 60 = 360
30x = 360 - 60
30x = 300
x = 300/30
x = 10
So, the value of x is 10.
To find the value of x, we need to use the fact that the sum of the exterior angles of any polygon is always 360 degrees.
In a regular decagon, there are 10 exterior angles, so the sum of all the exterior angles is 10 * (3x + 6)°.
Since the sum of the exterior angles is 360 degrees, we can set up the following equation:
10 * (3x + 6) = 360
Now, let's solve the equation for x.
Divide both sides of the equation by 10:
(3x + 6) = 360 / 10
Simplify:
3x + 6 = 36
Subtract 6 from both sides of the equation:
3x = 36 - 6
Simplify:
3x = 30
Finally, divide both sides of the equation by 3 to solve for x:
x = 30 / 3
Simplify:
x = 10
Therefore, the value of x is 10.
the exterior angles of a decagon are all 360/10 = 36°
So,
3x+6 = 36
x = 10
For the interior angles (each 144°),
3x+6 = 144
x = 46