Given the following angles of a regular polygon, 120°, (3x+5)°, (x)°, 45°, 135°, (x-45)°, and (5x)°, what is the value of x?
the sum of the angles of an n-sided polygon is 180(n-2). So your angles must add up to 180*5 = 900°
So add 'em up and solve for x.
To find the value of x in this problem, we need to use the fact that the sum of the interior angles of a regular polygon is given by (n-2) * 180 degrees, where n is the number of sides of the polygon.
In this case, we have the following angles given: 120°, (3x+5)°, (x)°, 45°, 135°, (x-45)°, and (5x)°. We can add up these angles to get the total sum of the interior angles.
Sum of interior angles = 120° + (3x+5)° + (x)° + 45° + 135° + (x-45)° + (5x)°
Now, according to the formula mentioned earlier, the sum of the interior angles of a regular polygon with n sides is (n-2) * 180 degrees. In this case, since the polygon is regular, all the interior angles are equal.
So we can equate the sum of the interior angles calculated above to (n-2) * 180 degrees, where n is the number of sides of the polygon.
120° + (3x+5)° + (x)° + 45° + 135° + (x-45)° + (5x)° = (n-2) * 180°
Simplifying this equation will give us an equation in terms of x, which we can solve to find the value of x.