Question

find the measure of \\( \angle g m k \\).
\\( m \angle g m k = \\) submit

Explanation:

Step1: Set angles equal

$22x + 4 = 96 - 2x$

Step2: Solve for x

$22x + 2x = 96 - 4$
$24x = 92$
$x = \frac{92}{24} = \frac{23}{6}$

Step3: Calculate ∠GMK

$96 - 2(\frac{23}{6}) = 96 - \frac{23}{3} = \frac{288 - 23}{3} = \frac{265}{3} ≈ 88.33$

Wait, correction: Parallel lines mean corresponding angles equal, so 22x+4=96-2x → 24x=92 → x=92/24=23/6≈3.833. Then ∠GMK=96-2*(23/6)=96-23/3=(288-23)/3=265/3≈88.33. But maybe integer? Check if angles are supplementary? No, parallel lines cut by transversal: corresponding angles equal. So yes, 265/3 or 88.33°.

Answer:

$\frac{265}{3}$ (or approximately 88.33)