Question

1. if m∠dge=(6x - 5)°, m∠egf=(12x + 11)°, m∠fgd = 33°. what is x?

Explanation:

Step1: Set up equation based on angle - sum

Assume the sum of the angles around point G is 180°. So, \((6x - 5)+(12x + 11)+33=180\).

Step2: Combine like - terms

Combine the x - terms and the constant terms: \((6x+12x)+(- 5 + 11+33)=180\), which simplifies to \(18x + 39=180\).

Step3: Isolate the variable term

Subtract 39 from both sides of the equation: \(18x=180 - 39\), so \(18x=141\).

Step4: Solve for x

Divide both sides by 18: \(x=\frac{141}{18}=\frac{47}{6}\approx7.83\).

Answer:

\(x = \frac{47}{6}\)