Question

what is the value of x? (with a diagram of two transversal lines intersecting a horizontal line, angles labeled: 2, 4, 107°, 8, 1, 6x + 5, 5, 7)

Explanation:

Step1: Identify supplementary angle

The angle $107^\circ$ and $\angle 5$ are supplementary, so:
$\angle 5 = 180^\circ - 107^\circ = 73^\circ$

Step2: Set equal to congruent angle

$\angle 5$ and $6x+5$ are corresponding angles (congruent):
$6x + 5 = 73$

Step3: Solve for x

Subtract 5 from both sides:
$6x = 73 - 5 = 68$
Divide by 6:
$x = \frac{68}{6} = \frac{34}{3} \approx 11.33$

Answer:

$x = \frac{34}{3}$ or $x \approx 11.33$