To find the measure of angle C in triangle ABC, we can use the Law of Cosines, which states that for any triangle with sides a, b, and c and opposite angles A, B, and C:c^2 = a^2 + b^2 - 2abcos(C)In this case, we know that AB = 7, BC = 8, and AC = 9. Plugging these values into the Law of Cosines equation and solving for cos(C), we get:cos(C) = (7^2 + 9^2 - 8^2) / (2 * 7 * 9)
cos(C) = 0.6111111Taking the inverse cosine (cos^-1) of 0.6111111, we get the angle C:C = cos^-1(0.6111111)
C ≈ 51.96 degreesTherefore, to the nearest degree, m∠C ≈ 52 degrees.