We know, the sum of all the angle in an triangle is 180,
So, We can calculate adjacent angle of angle 1,
Let, that adjacent angle = b
So, 34 + 103 + b = 180
b = 180 - 137
b = 43
Now, angle b forms linear pair with angle a, so their sum would be 180
a + b = 180
a + 43 = 180
a = 180 - 43
a = 137
In short, Your Answer would be Option C
Hope this helps!