Lines and are two distinct lines in a plane

MATHEMATICS · Multi-part · CBSE · Mathematics · Lines and Angles · Lines and Angles

Problem

Lines

r

and

s

are two distinct lines in a plane. A transversal

u

intersects them at points

P

and

Q

respectively. At

P

, the interior angle on the left of

u

equals

\angle a

, and at

Q

the interior angle on the right of

u

equals

\angle b

. It is given that

\angle a + \angle b = 180^\circ

. (a) Prove that lines

r

and

s

are parallel. (b) A second transversal

v

cuts the same lines

r

and

s

at points

M

and

N

respectively. At

M

, the alternate interior angle on the left of

v

measures

(2y + 15)^\circ

and at

N

its alternate interior partner measures

(5y - 45)^\circ

. Find the value of

y

. (c) Using the value of

y

, calculate the measure of an exterior angle on the upper right side at point

N