Mathematics

Problem

Lines

p

and

q

are parallel. Two distinct transversals

r

and

s

intersect

p

P

and

R

respectively, and intersect

q

Q

and

S

respectively. The transversals meet each other at point

O

situated between

p

and

q

. At point

P

the interior angle between

p

and

r

(2x + 5)^{\circ}

, while at point

Q

the corresponding exterior angle between

q

and

r

113^{\circ}

. At point

R

the exterior angle between

p

and

s

(3y - 7)^{\circ}

, and at point

S

the interior angle on the same side of

s

149^{\circ}

. a. (a) Find the value of

x

. b. (b) Using the obtained value of

x

, determine the value of

y

. c. (c) Hence calculate the acute angle between the two transversals

r

and

s

. Explain every step of your working.