Mathematics

Problem

Lines

a

and

b

are parallel. Transversal

m

meets them at points

P

and

Q

, while transversal

n

meets them at points

R

and

S

. The following angle measures are given: • On transversal

m

, the alternate exterior angles at

P

and

Q

are

(5x - 3y)^{\circ}

and

(2x + y + 30)^{\circ}

respectively. • On transversal

n

, the corresponding angle at

R

(3x + 2y - 10)^{\circ}

and the corresponding angle at

S

110^{\circ}

. a. (i) Form two independent equations in

x

and

y

using the angle relationships described. b. (ii) Solve the simultaneous equations to obtain the values of

x

and

y

. c. (iii) Hence calculate the measure of each of the alternate exterior angles on transversal

m