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BCG =65

Step-by-step explanation:

DCG + GCB = DCB

We know BCG = 31x+3 and GCD = 12x+2  and BCD = 91

Substituting these in

12x+2 + 31x+3 = 91

Combine like terms

43x +5 = 91

Subtract 5 from each side

43x+5-5 = 91-5

43x = 86

Divide by 43

43x/43= 86/43

x=2

BCG = 31x+3

        =31(2)+3

         =62+3

           =65

m∠BCD = m∠BCG + m∠GCD

We have m∠BCG = 31x + 3, m∠GCD = 12x + 2 and m∠BCD = 91°. Substitute:

91 = (31x + 3) + (12x + 2)

91 = (31x + 12x) + (3 + 2)

91 = 43x + 5       subtract 5 from both sides

86 = 43x       divide both sides by 43

2 = x

m∠BCG = 31x + 3 → m∠BCG = 31(2) + 3 = 62 + 3 = 65

for this case we have by definition, if two lines are perpendicular, then the product of their slopes is -1.

then, given the following line:

so,

we are looking for m_ {2}:

then, the line is given by:

we find "b" replacing the given point:

finally, the equation is:

option c