Final answer:
The measure of angle A is approximately 66°.
Step-by-step explanation:
Given that Angle B is 102°, AC = 16, and AB = 7, we can use the Law of Cosines to find the measure of angle A. The Law of Cosines states that for any triangle with sides a, b, and c, and opposite angles A, B, and C respectively, the following equation holds:
c^2 = a^2 + b^2 - 2ab*cos(C)
In this case, we want to find angle A, so we can rearrange the equation as follows:
cos(A) = (b^2 + c^2 - a^2) / 2bc
Plugging in the values we have:
cos(A) = (7^2 + 16^2 - 2*7*16*cos(102°)) / (2*7*16)
Solving for A, we get approximately A ≈ 66°. Therefore, the answer is (c) 66°.