Answer:
The answer to your question is below
Step-by-step explanation:
I numbered the squares, see the picture below
Angle 3 and the angle given are vertical angles so they measure the same
       angle 3 = 137°
The sum of the angles 1, 2, 3 and 137 equals 360°, so
 angle 1 + 137 + angle 3 + 137 = 360
  and angle 1 and 3 are vertical angles so angle 1 = angle 3
  2angle 1 = 360 - 137 -137
  2 angle 1 = 86
    angle 1 = 86 /2
    angle 1 = 43°
    angle 2 = 43°
The angle given and the angle 5 are corresponding angles, they measure the same
    angle 5 = 137°
Angle 5 and 6 are vertical angles, they measure the same
    angle 6 = 137°
Angle 2 and angle 7 are corresponding angles, they measure the same
    angle 7 = 43°
Angle 3 and angle 6 are corresponding angles
     angle 6 = 137°
Angle 4 and 7 are vertical angle, so they measure the same
     angle 4 = 43°
