Line intersects two distinct lines and at points and respectively

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

Problem

Line

x

intersects two distinct lines

l

and

m

at points

P

and

Q

respectively. The angle between

l

and

x

on the upper right side of

x

is equal to the angle between

m

and

x

on the upper right side of

x

. Each of these equal angles measures

68^{\circ}

. (i) Prove that

l \parallel m

. (ii) Calculate the measure of the interior angle on the lower left side of

x

at point

Q

, clearly stating your reasons.