Question

ae and df are parallel. if m∠abg = 12x and m∠hcf = 11x + 9, what is m∠hcf?

Explanation:

Step1: Use the property of parallel lines

Since \(\overline{AE}\parallel\overline{DF}\), \(\angle ABG\) and \(\angle HCF\) are corresponding angles. Corresponding angles are equal, so \(12x = 11x+9\).

Step2: Solve the equation for \(x\)

Subtract \(11x\) from both sides of the equation \(12x = 11x + 9\).
\(12x-11x=11x + 9-11x\)
\(x = 9\)

Step3: Find \(m\angle HCF\)

Substitute \(x = 9\) into the expression for \(m\angle HCF\) (\(m\angle HCF=11x + 9\)).
\(m\angle HCF=11\times9+9=(11 + 1)\times9=12\times9 = 108^{\circ}\)

Answer:

\(108^{\circ}\)