Question

Need help, show work on a piece of paperon problem 8

Answer 1

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