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
Answer: m∠BCG = 65°
