Mathematics

Problem

Lines

m

and

n

are cut by a transversal

t

at points

A

and

B

respectively. At

A

, the angle on the right of

t

and between the two lines (interior region) measures

120^{\circ}

. At

B

, the angle on the right of

t

and between the two lines is denoted by

x^{\circ}

. a. (i) Name the special pair of angles formed at

A

and

B

with respect to the transversal. b. (ii) If

m \parallel n

, calculate the value of

x

and write the reason for each step of your calculation. c. (iii) Conversely, if

x=60^{\circ}

, explain whether this information alone is sufficient to conclude that

m \parallel n

. State the theorem you use in your explanation.