Question

find the measure of \\( \angle kcf \\).

Explanation:

Step1: Use the property of linear pair

Since \(\angle GCF\) and \(\angle FCK\) form a linear pair, \(\angle GCF+\angle FCK = 180^{\circ}\).
Given \(\angle GCF=7f + 123\) and \(\angle FCK=7f+169\), we have \((7f + 123)+(7f+169)=180\).

Step2: Solve the equation for \(f\)

Combine like - terms: \(14f+292 = 180\).
Subtract 292 from both sides: \(14f=180 - 292=- 112\).
Divide both sides by 14: \(f=\frac{-112}{14}=-8\).

Step3: Find the measure of \(\angle KCF\)

Substitute \(f = - 8\) into the expression for \(\angle KCF\) (\(\angle KCF=7f + 169\)).
\(\angle KCF=7\times(-8)+169\).
First, calculate \(7\times(-8)=-56\).
Then, \(\angle KCF=-56 + 169 = 113^{\circ}\).

Answer:

\(113^{\circ}\)