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To find the measure of segment AB, you can use the Law of Sines.
First, determine the measure of angle C:
m∠C = 180° - (m∠A + m∠B)
m∠C = 180° - (55° + 44°)
m∠C = 180° - 99°
m∠C = 81°
Use the Law of Sines formula:
a/sin A = b/sin B = c/sin C
Substitute the known values:
AB/sin 55° = 68/sin 44°
Now, solve for AB:
AB = 68 * sin 55° / sin 44°
AB ≈ 81.12
Therefore, the measure of segment AB is 81.12.