Question

find the measure of (angle gbf).

Explanation:

Step1: Use the property of linear pair

Angles \( \angle GBF\) and \( \angle PBF\) form a linear pair. So, \((6k + 115)+(5k + 21)=180\).

Step2: Solve the equation for \(k\)

Combine like - terms: \(6k+5k+115 + 21=180\), which simplifies to \(11k+136 = 180\).
Subtract 136 from both sides: \(11k=180 - 136\), so \(11k = 44\).
Divide both sides by 11: \(k=\frac{44}{11}=4\).

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

Substitute \(k = 4\) into the expression for \( \angle GBF\) (\(6k + 115\)).
\(6k+115=6\times4+115\).
First, calculate \(6\times4 = 24\). Then \(24+115=139\).

Answer:

\(139^{\circ}\)