Solve the triangle with the given parts. \[ a=21.5 m, b=15.3 m, c=6.3 m \] What is the degree measure of angle A? \[ 167.9^{\circ} \] (Round to the nearest tenth as needed.) What is the degree measure of angle $B$ ? (Round to the nearest tenth as needed.)

Step 1 ：We are given the lengths of all three sides of a triangle and we are asked to find the degree measure of angle A and B. We can use the Law of Cosines to find the degree measure of angle A and B. The Law of Cosines states that for any triangle with sides of lengths a, b, and c, and an angle A opposite side a, the following equation holds: \[a^2 = b^2 + c^2 - 2bc \cos(A)\]

Step 2 ：We can rearrange this equation to solve for cos(A): \[\cos(A) = \frac{b^2 + c^2 - a^2}{2bc}\]

Step 3 ：Then we can use the inverse cosine function to find the degree measure of angle A: \[A = \cos^{-1}\left(\frac{b^2 + c^2 - a^2}{2bc}\right)\]

Step 4 ：We can use a similar process to find the degree measure of angle B. The Law of Cosines for angle B is: \[b^2 = a^2 + c^2 - 2ac \cos(B)\]

Step 5 ：We can rearrange this equation to solve for cos(B): \[\cos(B) = \frac{a^2 + c^2 - b^2}{2ac}\]

Step 6 ：Then we can use the inverse cosine function to find the degree measure of angle B: \[B = \cos^{-1}\left(\frac{a^2 + c^2 - b^2}{2ac}\right)\]

Step 7 ：Given that a = 21.5, b = 15.3, c = 6.3, we can substitute these values into the equations to find the degree measure of angle A and B.

Step 8 ：Substituting the values into the equation for cos(A), we get cos_A = -0.9776429090154579

Step 9 ：Substituting the values into the equation for cos(B), we get cos_B = 0.9887412329272794

Step 10 ：Using the inverse cosine function, we find that A = 167.9 and B = 8.6

Step 11 ：Final Answer: The degree measure of angle A is \(\boxed{167.9^\circ}\) and the degree measure of angle B is \(\boxed{8.6^\circ}\)