The exterior angles of an octagon are 2x degrees,half x degrees,(x+40 degrees),110 degrees,135 degrees,160 degrees,(2x+10 degrees) and 185 degrees.find the value of x?
all the exterior angles add up to 360°, so add up all those expressions and solve for x.
2x + x/2 + ... + 185 = 360
.... but the 4 constant angles given already add up to 590°
which means that the value of x must be negative.
i.e. x = -50.9°
The octagon must be concave.
It just said to find x, so ok then.
To find the value of x, we can use the property that the sum of all exterior angles of a polygon is always 360 degrees.
Step 1: Sum up all the given exterior angles
2x + (1/2)x + (x + 40) + 110 + 135 + 160 + (2x + 10) + 185 = 360
Simplifying the equation:
6x + (3/2)x + 375 = 360
Combining like terms:
(15/2)x + 375 = 360
Step 2: Solve the equation for x
(15/2)x = 360 - 375
(15/2)x = -15
Multiply both sides by 2/15:
x = (-15) * (2/15)
x = -2
Therefore, the value of x is -2.