Question

what is the value of x? (the image shows intersecting lines with angle expressions 3x + 17 and 3x + 1, and other angle labels 7, 8, 6, 3, 4, 1)

Explanation:

Step1: Identify vertical angles

$\angle 7 = 3x+1$, $\angle 6 = 3x+17$

Step2: Use linear pair property

$\angle 7 + \angle 6 = 180^\circ$
$(3x+1)+(3x+17)=180$

Step3: Simplify the equation

$6x + 18 = 180$

Step4: Solve for x

$6x = 180-18$
$6x = 162$
$x = \frac{162}{6}$

Answer:

$27$