Lines and are parallel and are intersected by a transversal

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

Problem

Lines

l

and

m

are parallel and are intersected by a transversal

t

. At the point where

t

meets

l

, the acute angle lying inside the region between

l

and

m

measures

(4x + 15)^{\circ}

. At the point where

t

meets

m

, the alternate interior angle on the same side of the transversal measures

(7x - 9)^{\circ}

. (i) Find the value of

x

. (ii) Using this value of

x

, determine the measure of each of the eight angles formed by

t

with the two parallel lines. For every angle calculated, clearly state the angle–pair relationship you have applied.