Lines and are cut by a transversal

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

Problem

Lines

m

and

n

are cut by a transversal

t

. The pair of alternate interior angles on the right of the transversal are

\left(\dfrac{7x}{2} - 13\right)^{\circ}

and

\left(\dfrac{5x}{3} + 11\right)^{\circ}

respectively. (a) Assuming that

m \parallel n

, find the value of

x

and the measure of each of the alternate interior angles. (b) The lines

m

and

n

will not be parallel if the two alternate interior angles are unequal. For integral values of

x

between

-10

and

40

, list all values for which

m

and

n

are not parallel, giving reasons for your answer.