Question

If two vertical angles are labeled 14x + 12 and 6x + 36, then the value of x is (blank) and each angle measures (blank) degrees.

Options:
A) x = 3; each angle measures 60 degrees
B) x = 4; each angle measures 72 degrees
C) x = 5; each angle measures 84 degrees
D) x = 6; each angle measures 96 degrees

Answer 1

The value of x is 3, and by substituting this value back into the expressions for the vertical angles, it's determined that each angle measures 54 degrees.

Step-by-step explanation:

To determine the value of x when two vertical angles are labeled 14x + 12 and 6x + 36, we need to understand that vertical angles are equal. This means we can set the expressions for the two angles equal to each other and solve for x.

Step-by-Step Solution:

1. Set the two angles equal to each other: 14x + 12 = 6x + 36.
2. Subtract 6x from both sides: 8x + 12 = 36.
3. Subtract 12 from both sides: 8x = 24.
4. Divide by 8 to find the value of x: x = 3.
5. Substitute x back into either original angle expression to find the measure of each angle: 14(3) + 12 = 54 degrees.

Therefore, the value of x is 3, and each angle measures 54 degrees.