Question

The measures of two angles are (4x+8) and (2x - 20). What is the value of x if these angles are congruent?

Options:
A) x = 6
B) x = 12
C) x = 4
D) x = 10

Answer 1

To solve for x when angles (4x+8) and (2x-20) are congruent, we equate the two expressions and solve the resulting equation. The solution to the equation is x = -14, which does not match any of the provided options.

Step-by-step explanation:

To determine the value of x if the angles (4x+8) and (2x - 20) are congruent, we set the two expressions equal to each other because congruent angles have the same measure. The equation to solve is 4x + 8 = 2x - 20.

Here are the steps to solve the equation:

1. Subtract 2x from both sides: 4x + 8 - 2x = 2x - 20 - 2x, which simplifies to 2x + 8 = -20.
2. Subtract 8 from both sides: 2x + 8 - 8 = -20 - 8, simplifying to 2x = -28.
3. Divide both sides by 2: 2x / 2 = -28 / 2, which simplifies to x = -14.

However, none of the options given (A) x = 6, (B) x = 12, (C) x = 4, (D) x = 10 match the calculated value of x. There may be a mistake either in the question or in the options provided.