Part 1
By angle addition property
m<4+m<5+m<1=180 degrees
m<4=39 degrees
m<5=45 degrees
substitute
39+45+m<1=180
m<1=180-39-45
m<1=96 degrees
Part 2
we see that
m<4 and m<3 are alternate interior angles
and since lines, l and k are parallel, <4 and <3 are congruent
so
m<3=39 degrees
Part 3
we see that <2 and <5 are alternate interior angles
and since lines, l and k are parallel, < 2 and <5 are congruent
so m<2=45 degrees
Part 4
therefore m<1+m<2+m<3=180 degrees
The relationship between <1, <2 and <3 is an example of the following rule
The sum of the interior angles measures of a triangle is 180 degrees