Two straight railway tracks are represented by the parallel lines and

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

Problem

Two straight railway tracks are represented by the parallel lines

T_1

and

T_2

. A signal mast standing between them acts as a transversal. The two consecutive interior angles formed between the mast and the tracks have measures

\left(\dfrac{6x}{5} + 8\right)^{\circ}

and

\left(\dfrac{4x}{3} - 2\right)^{\circ}

. (i) Write an equation in

x

using the relationship between these two angles. (ii) Solve the equation to find the value of

x

. (iii) Determine the measure of each of the consecutive interior angles. (iv) Verify that the two angles are supplementary.