Using the cosine rule: c2=a2+b2-2abcosC=16+169-104cos45=185-52√2=111.46 approx, so c=10.56 approx. (cos45=sin45=√2/2.)
Sine rule: sinA/a=sinB/b=sinC/c, sinA/4=sinC/c=(√2/2)/10.56,
sinA=2√2/10.56=0.2679, making A=15.54° approx, which is 16° to the nearest degree.