One angle measures 150°, and another angle measures (2k + 88)°. If the angles are vertical angles, determine the value of k.

Question

k = 12
k = 31
k = 62
k = 75

Answer 1

Vertical angles are equal, which means that if one angle measures 150°, then the other angle, which measures \((2k + 88)°\), must also equal 150°.

We can set up the equation:

\[ 2k + 88 = 150 \]

Now, we'll solve for \(k\):

1. Subtract 88 from both sides:

\[ 2k = 150 - 88 \] \[ 2k = 62 \]

2. Divide both sides by 2:

\[ k = \frac{62}{2} \] \[ k = 31 \]

Thus, the value of \(k\) is 31.