Question

what is the value of k?
o k = 28
o k = 29
o k = 31
o k = 42

Explanation:

Step1: Use the linear - pair property

Since \((5k - 3)^{\circ}\) and \((9 + k)^{\circ}\) form a linear pair, their sum is \(180^{\circ}\). So, \((5k-3)+(9 + k)=180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(5k-3 + 9 + k=(5k + k)+(-3 + 9)=6k+6\). The equation becomes \(6k + 6=180\).

Step3: Solve for \(k\)

Subtract \(6\) from both sides: \(6k+6-6=180 - 6\), which gives \(6k=174\). Then divide both sides by \(6\): \(k=\frac{174}{6}=29\).

Answer:

\(k = 29\)