The angle whose tangent equals 6/8 in triangle GIH is angle G.
Two figures are said to be similar if they have the same shape and the ratio of their corresponding sides are in the same proportion.
Triangle GIH is similar to triangle KJL, hence the ratio of their corresponding sides are in the same proportion and their corresponding angles are congruent.
Hence:
JLcorresponds to IH and LK corresponds to GH. Hence:
tanG = tanK = 6/8
The angle whose tangent equals 6/8 in triangle GIH is angle G.
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