Mathematics

Problem

Lines

g

and

h

are parallel. A transversal

k

intersects them at points

R

and

S

. On the right side of

k

, the consecutive interior angles at

R

and

S

measure

(4z + 15)^\circ

and

(2z + 45)^\circ

respectively. a. (i) State the relationship between these two consecutive interior angles. b. (ii) Using the relationship, find the value of

z

. c. (iii) Calculate the measure of the exterior angle at

R

on the right of the transversal.