Question

Is my paragraph correct for this proof?
What I have to prove is that angle 4 is equal to the measure of angle 8.

My paragraph:
PQ is parallel to RS because of construction. <2 = <8 based on the alternate exterior angles theorem. <8 + <7 = 180 due to the definition of supplementary angles. <4 + <1 = 180 because of the definition of supplementary angles. <2 + <7 = 180 using the substitution property of equality, <2 = <8. <4 + <1 = <2 + <7 because of the transitive property of equality. <4 = <8 when using the subtraction property of equality, making them congruent.