Question

Astronomers sometimes use angle measures divided into degrees,minutes,seconds one degree is equal to 60 seconds suppose that ∠j is 48 degrees , 26 minutes 8 seconds what is the measure of ∠k?

Answer 1

Ok, there are two scenarios here.

1) It's a typo and "<K" should be written as "<J"

if that is the case, we can convert from degrees,minutes,seconds >> degrees like so

$48 + \frac{26}{60} + \frac{8}{3600}$

once calculated, we get 48.43 degrees.

scenario 2)

<k is the third angle in a right triangle

this would mean that <j + <K + 90 = 180

from the first example, we know that <J = 48.43 degrees

Therefor 

48.43 + <k + 90 = 180

48.43 + 90 = 138.43

so 

138.43 + <k = 180


Therefor, <K = 41.57 degrees

I really hope this helps!!:)