Question

Look at this diagram:

C
D
E
F
G
H
I
J


If
DF
and
GI
are parallel lines and mIHE = 61°, what is mGHJ?

Answer 1

I can’t be sure of the exact connections from the single column of letters — could you upload or describe which points are joined by which segments (which points lie on the two parallel lines, and which segments meet at H)?

If the intended picture is the usual one where G and I lie on one line, D and F on the other parallel line, and the two transversals through H meet those parallel lines at G/I and D/F (so HI and HG go to the same parallel line and HE and HJ go to the other), then ∠IHE and ∠GHJ are corresponding (or congruent alternate interior) angles, so

m∠GHJ = m∠IHE = 61°.

If the picture is different (for example one of the angles given and the one asked are interior/exterior supplements) the answer could be 119° instead. Send the diagram or a brief description of which points are connected and I’ll confirm.