Since lines p and q are parallel
Since line t intersect them, then
<2 and the angle of measure 55 degrees are corresponding angles
Since the corresponding angles are equal in measures, then
m < 2 = 55 degrees
Since < 2 and < 4 form a pair of linear angles
Since the sum of the measures of the linear angles is 180 degrees, then
m < 2 + m < 4 = 180
55 + m < 4 = 180
Subtract 55 from both sides
55 - 55 + m < 4 = 180 - 55
m < 4 = 125 degrees
Since < 4 and < 5 are alternate angles
Since alternate angles are equal in measures, then
m < 4 = m < 5
m < 5 = 125 degrees