Mathematics

Problem

Lines

p

and

q

are parallel. Two distinct transversals

r

and

s

intersect them between the parallel lines. Transversal

r

meets

p

M

and

q

N

. Transversal

s

meets

p

P

and

q

Q

. a. (i) The angle between

p

and

r

M

on the upper left side is

58^{\circ}

. Calculate the angle between

q

and

r

N

that lies on the lower left side. b. (ii) The angle between

p

and

s

P

on the upper left side is

118^{\circ}

. Find the angle between

q

and

s

Q

on the lower right side.