Question

what is the value of k?
○ k=28
○ k=29
○ k=31
○ k=42
(5k - 3)° (9 + k)°

Explanation:

Step1: Identify supplementary angles

The two angles \((5k - 3)^\circ\) and \((9 + k)^\circ\) are supplementary (they form a linear pair), so their sum is \(180^\circ\).
\[
(5k - 3) + (9 + k) = 180
\]

Step2: Combine like terms

Combine the \(k\) terms and the constant terms:
\[
5k + k - 3 + 9 = 180 \\
6k + 6 = 180
\]

Step3: Solve for \(k\)

Subtract 6 from both sides:
\[
6k = 180 - 6 \\
6k = 174
\]
Divide both sides by 6:
\[
k = \frac{174}{6} \\
k = 29
\]

Answer:

\(k = 29\) (corresponding to the option \(k = 29\))