Question

look at this diagram: if bd and eg are parallel lines and m∠gfc = 115°, what is m∠bcf?

Explanation:

Step1: Recall linear - pair property

Linear - pair angles are supplementary, meaning they add up to 180°. ∠GFC and ∠BCF are a linear - pair of angles.
Let \(m\angle GFC = 115^{\circ}\) and \(m\angle BCF=x\).
We know that \(m\angle GFC + m\angle BCF=180^{\circ}\).

Step2: Solve for \(m\angle BCF\)

Substitute the value of \(m\angle GFC\) into the equation:
\(115^{\circ}+x = 180^{\circ}\)
\(x=180^{\circ}- 115^{\circ}\)
\(x = 65^{\circ}\)

Answer:

\(65^{\circ}\)