One angle measures 150°, and another angle measures (2k + 88)°. If the angles are vertical angles, determine the value of k.
a) k = 12
b) k = 31
c) k = 62
d) k = 75
Vertical angles are pairs of angles that are opposite each other when two lines intersect. They are always congruent, meaning they have the same measure.
In this case, we know that one angle measures 150°. The other angle measures (2k + 88)°. Since they are vertical angles, they must have the same measure.
Therefore, we can set up the equation:
150° = (2k + 88)°
Subtract 88 from both sides of the equation:
150° - 88° = 2k°
62° = 2k°
Divide both sides of the equation by 2:
31° = k°
Therefore, k = 31.
So, the value of k is k = 31.
The correct answer is b) k = 31.