Mathematics

Problem

A civil engineer is designing two straight service roads

R_1

and

R_2

that are intended to be parallel. To check the design, she draws a straight reference line

T

that cuts

R_1

at point

A

and

R_2

at point

B

. At point

A

, the angle between

T

and

R_1

, measured to the left of

T

, is

(3y+15)^\circ

. At point

B

, the angle between

T

and

R_2

, measured to the right of

T

, is

(6y-33)^\circ

. Solve the following parts. a. (i) Using the requirement that

R_1

and

R_2

be parallel, find the value of

y

. b. (ii) After finding

y

, prove that

R_1

and

R_2

are parallel by citing an appropriate pair of angles. c. (iii) Calculate the measures of all eight angles formed by the intersection of

T

with

R_1

and

R_2