Question

one angle measures 170°, and another angle measures (6k + 44)°. if the angles are vertical angles, determine the value of k.
options:
k = 12
k = 20
k = 21
k = 126

Explanation:

Step1: Use the property of vertical angles

Vertical angles are equal. So, we set up the equation \(170 = 6k + 44\).

Step2: Solve the equation for \(k\)

Subtract \(44\) from both sides: \(170-44=6k + 44-44\), which simplifies to \(126 = 6k\).
Then divide both sides by \(6\): \(\frac{126}{6}=\frac{6k}{6}\), so \(k = 21\).

Answer:

\(k = 21\)