Question

For the diagram below, if < 4 = 2x - 6, and < 6 = x + 14, what is the value of x?

Answer 1

In the figure, ∠4 and ∠6 are alternate interior angles. Given that lines a and b are parallel to each other, then ∠4 and ∠6 must be congruent. So to solve for x, we use the equation:

`2x-6=x+14`

We simplify the equation to get x.

`\begin{gathered} 2x-6=x+14 \\ 2x-x=14+6 \\ x=20 \end{gathered}`

The answer is option D, 20.