how many seconds are in one degree explain?

Degrees, Minutes, Seconds is analogous to Hours, Minutes, Seconds.

There are 60 minutes in an hour : there are 60 minutes in a degree

There are 3600 seconds in an hour : there are 3600 seconds in a degree.

28 degrees 42 seconds = 28 + 42/3600 = 28.012 degrees

Complimentary:

90 - 28.012 = 61.988°

Supplementary:

180 - 28.012 = 151.988°

Happy mathing!

Something Clever and Robert have both given excellent explanations, and using what they have said, will permit you to work degrees, minutes, and seconds, with fluency.

But I wish to point out a discrepancy in the way you've written the question. You have:

28 degrees and 42' seconds

But by itself, 42' means 42 minutes.

42 seconds would be written, 42".

And if it was really meant to be seconds, usually (though not always!) minutes would be included:

28º 0' 42"

So you just need to be careful about whether the 42 you have there, is really meant to be minutes or seconds.

PS: Sometimes, these are referred to as "arc minutes" and "arc seconds," just to distinguish them from their temporal counterparts, especially when dealing with angles less than a degree, when no degrees are included in the amount of the angle.

For the second question, the complementary angle of 28 deg 42 sec is 90 - 28 deg 42 sec

You have to rewrite 90 deg as 89 deg 59 min 60 sec, from which you subtract 28 deg 0 min 42 sec,

and get 61 deg 59 min 18 sec.

The supplement is 90 more than the complement, so it's 151 deg 59 min 18 sec

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