Example 5 Given m angle7=38^ and m angle10=102^ the measure of each missing angle

angle 1 - 78
angle 2- 102
angle 3- 78
angle 4- 102
angle 5- 38
angle 6- 142
angle 8- 142
angle 9- 78
angle 11- 78
angle 12- 102
angle 13- 38
angle 14- 142
angle 15- 38
angle 16- 142