step 1
Find the measure of angle 2
we have that
127+m<2=180 -----> by form a linear pair
so
m<2=180-127
m<2=53 degrees
step 2
Find out the measure of angle 4
we have that
m<4=59 -----> by corresponding angles
step 3
Find the measure of angle 5
we have that
m<5+m<4=180 -----> by form a linear pair
so
m<5+59=180
m<5=180-59
m<5=21 degrees
step 4
Find the measure of angle 1
REmember that
The sum of the interior angles in any quadrilateral must be equal to 360 degrees
so
m<1+127+m<5+59=360
m<1+127+21+59=360
m<1+207=360
m<1=153 degrees
step 5
Find the measure of angle 3
we have that
the sum of the interior angles in any triangle must be equal to 180 degrees
In the smaller triangle
m<2+m<3+m<4=180
substitute the given values
53+m<3+59=180
m<3+112=180
m<3=68 degrees