A) using theorems pertaining to transverals and parallel lines, prove that m∠1 + m∠2 = 180o
b) find the value of x.

A) Two parallel lines, intersecting a 3rd line (a traversal), indicates that two same-sided, internal angles MUST be SUPPLEMENTARY (sum, or add up to 180°).

b) Since <1 and <2 are supplementary, they add up to 180°. Therefore, <1 + <2 = 180:
(20x+5) + (24x-1) = 180
44x + 4 = 180
44x + 4 -4 = 180-4
44x = 176
44x/44 = 176/44
x = 4

(1/x + 1)^2 + 6 (1/x + 1) +5