Question

find the measure of ∠gmk.

image of a coordinate-like diagram with lines and angles: horizontal lines hi (with h left, i right) and jk (with j left, k right), vertical line fg (with f top, g bottom) intersecting them at l (on hi) and m (on jk). angle at l on hi: (22x + 4)°, angle at m on jk: (96 - 2x)°. then m∠gmk = °

Explanation:

Step1: Identify parallel lines and transversal

HL || JK, FG is transversal → corresponding angles equal: $22x + 4 = 96 - 2x$

Step2: Solve for x

$22x + 2x = 96 - 4$ → $24x = 92$ → $x = \frac{92}{24} = \frac{23}{6} \approx 3.833$

Step3: Calculate ∠GMK

Substitute x into $96 - 2x$: $96 - 2(\frac{23}{6}) = 96 - \frac{23}{3} = \frac{288 - 23}{3} = \frac{265}{3} \approx 88.33^\circ$ (Note: If angles are supplementary, $22x+4+96-2x=180$ → $20x=80$ → $x=4$ → $96-8=88^\circ$. Likely parallel lines with supplementary adjacent angles correction: adjacent angles on straight line sum to 180)
Correct Step2: Adjacent angles sum to 180 → $22x+4+96-2x=180$ → $20x=80$ → $x=4$
Correct Step3: ∠GMK = $96 - 2(4) = 88^\circ$

Answer:

88