How do I find the measure of the angle?

[carolinepaz]

I'm a bit confused. If the picture doesn't show up, here's a link:

​< link to objectionable page removed >

I only know that G is 38 because 52+90 subracted from 180 is 38 and then the remaining angle is congruent to G. Would F be 104? Or 52?

 

[HallsofIvy]

Are we to assume that these are two pairs of parallel lines? That should be said as part of the problem. In that case we can use things like "alternate interior angles" or "alternate exterior angles" or "corresponding angles" on parallel lines are congruent.

Here, for example, the angle "f" and the angle formed by "e" and the 52 degree angle are "alternate interior angles". Since "e" is clearly a right angle, with measure 90 degrees, "f" has measure 90+ 52= 142 degrees.

It then follows that the "double" angle, with the two "congruent" signs, one of which is called "j", is also 142 degrees and so "j" (and its twin) has measure 142/2= 71 degrees.