The measure of angle z = degrees ( round to the nearest degree)

This is a perfect place to apply the Law of Cosines.  We want angle Z and know the length of the side opposite this angle:  9.7.

Law of Cosines is   c^2 = a^2 + b^2 - 2ab*cos C

Applied here, we get

9.7^2 = 6.8^2 + 14.7^2 - 2(6.8)(14.7)*cos Z

Then 

94.09 = 46.24 + 216.09 - 199.92*cos Z

Grouping the constant terms together:

-167.43 = -199.92*cos Z

Solving for cos Z:

0-.8374 = -cos Z
 
 0.8374 = cos Z
 
 Applying the inverse cosine function:  Z = 0.578 radians = 33 degrees          

The total would be 40.53

Idk i can’t read that