Lines and are parallel

MATHEMATICS · Subjective · CBSE · Mathematics · Lines and Angles · Lines and Angles

Problem

Lines

p

and

q

are parallel. Transversal

m

meets them at

A

(on

p

) and

B

(on

q

). Another transversal

n

meets them at

C

(on

p

) and

D

(on

q

). • At

A

, the angle between line

p

and transversal

m

above line

p

(2x + 12)^{\circ}

. • At

B

, the interior angle on the same side of

m

below line

q

(y + 8)^{\circ}

. Assume that the angles at

A

and

B

formed by transversal

m

are consecutive interior angles, so their measures add up to

180^{\circ}

. • At

C

, the angle between line

p

and transversal

n

above line

p

(3y - 4)^{\circ}

. • At

D

, the corresponding angle above line

q

68^{\circ}

. Determine the values of

x

and

y