The size of interior angles are 2x,1÷2x,x+40,2x+10,110,135,160,185find the value of x
The sum of interior angles of a polygon is given by the formula (n-2) x 180, where n is the number of sides of the polygon.
So, we can write the equation:
2x + 1/2x + x + 40 + 2x + 10 + 110 + 135 + 160 + 185 = (n-2) x 180
Simplifying, we get:
8.5x + 640 = (n-2) x 180
Since we know that the polygon has 10 sides (from the given number of angles), we can substitute n = 10, and solve for x:
8.5x + 640 = (10-2) x 180
8.5x + 640 = 1440
8.5x = 800
x = 94.12
Therefore, the value of x is approximately 94.12.