What is the answer to this question ?

If there is a really short way of doing this, I don't see it. The only way I know to do it is to find the third angle of both triangles. 

So for F the third angle for each of the pairs is
left side: 180 - (51 + 30) = 180 - 81 = 99
right side: 180 - (109 + 30) = 180 - 139 = 41
This is not the answer.

G
180 - (92 + 70) = 180 - 162 = 18
180 - (28 + 70) = 180 - 98 = 82
This is not the answer either.

H
180- (58 + 30) = 180 - (88) = 92
180 - (90  + 58) = 180 - 148 = 32
Not at all.

180 - (35 + 82) = 180 - 117 = 63
180 - (82 + 63) = 180 - 145 = 35
This pair has a third angle that is equal to the other triangle's pair. This is your answer.