Question

solve for the value of k.

Explanation:

Step1: Identify angle relationship

The two angles \((9k + 6)^\circ\) and \((4k + 5)^\circ\) are adjacent and form a linear pair, so their sum is \(180^\circ\). Thus, we set up the equation:
\((9k + 6)+(4k + 5)=180\)

Step2: Combine like terms

Combine the \(k\)-terms and the constant terms:
\(9k+4k + 6 + 5=180\)
\(13k+11 = 180\)

Step3: Solve for \(k\)

Subtract 11 from both sides:
\(13k=180 - 11\)
\(13k=169\)
Divide both sides by 13:
\(k=\frac{169}{13}\)
\(k = 13\)

Answer:

13