Mathematics

Problem

Line

p

is parallel to line

q

. They are intersected by a transversal

r

at points

M

and

N

respectively. At

M

the interior angle on the left of

r

is called

\angle A

, and at

N

the interior angle on the right of

r

is called

\angle B

. a. (i) State the positional relationship between

\angle A

and

\angle B

. b. (ii) Are these two angles equal or supplementary? Give a reason based on their position. c. (iii) If

\angle A = 112^\circ

, determine the measure of

\angle B

with justification. d. (iv) Explain why the sum of

\angle A

and the interior angle on the left of

r

N

180^\circ

. State clearly which angle pair property you have used.