Given
- ∠AOB = ∠COD = x² -2
- ∠BOC = 2x -10
- ∠AOD = ∠AOB + ∠BOC + ∠COD = 16x +2
Find
- x
- the measures of the angles
Solution
Substituting the given values of the angles into the given relaion, we get ...
... (x² -2) + (2x -10) + (x² -2) = 16x +2
... 2x^2 -14x -16 = 0 . . . . . subtract the right side (16x+2)
... 2(x +1)(x -8) = 0 . . . . . . .factor
Values of x that satisfy this equation are ...
... x = -1, x = 8
The value x = -1 does not give rise to positive angle values.
For x = 8, the angles are ...
... ∠AOB = ∠COD = 8²-2 = 62
... ∠BOC = 2·8 -10 = 6
... ∠AOD = 16·8 +2 = 130 . . . . = 62 +6 +62
The answer to the question not asked is ...
... x = 8; ∠AOB = ∠COD = 62; ∠BOC = 6; ∠AOD = 130
