Mathematics

Problem

Lines

p, q

and

r

are intersected by two different transversals. • Transversal

t

meets

p

and

q

, creating interior angles on the same side of

t

that measure

72^\circ

and

108^\circ

respectively. • Transversal

u

meets

q

and

r

, creating interior angles on the same side of

u

that measure

5z^\circ

and

(2z + 40)^\circ

respectively. If in each case the interior angles guarantee that the pair of lines they intersect are parallel, what is the value of

z

? a)

26

18

20

23