Question

1. given \\( \angle amr \\) \\( 12x - 18 \\) \\( \angle ymg \\) \\( 8x + 6 \\) find: 1) \\( x = \\) 2) \\( amr = \\) 3) \\( ymg = \\) image of intersecting lines at point m with angles labeled \\( 12x - 18 \\) and \\( 8x + 6 \\), and a table with what and why columns showing steps to solve for x

Explanation:

Step1: Set angles equal (vertical angles)

$12x - 18 = 8x + 6$

Step2: Isolate x terms (subtract 8x)

$12x - 8x - 18 = 6$
$4x - 18 = 6$

Step3: Isolate x (add 18)

$4x = 6 + 18$
$4x = 24$

Step4: Solve for x (divide by 4)

$x = \frac{24}{4}$

Step5: Calculate ∠AMR

$\angle AMR = 12x - 18 = 12(6) - 18$

Step6: Calculate ∠YMG

$\angle YMG = 8x + 6 = 8(6) + 6$

Answer:

1. $x = 6$
2. $\angle AMR = 54$
3. $\angle YMG = 54$