Lines are parallel and are intersected successively by a single transversal at points…

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

Problem

Lines

l_1, l_2, l_3

are parallel and are intersected successively by a single transversal

t

at points

A, B, C

(in that order). The angle between

t

and

l_1

A

(2x + 25)^{\circ}

, measured above

l_1

. The angle between

t

and

l_2

B

on the alternate interior side is

(3x - 5)^{\circ}

. (i) Find the value of

x

. (ii) Calculate the measure of the angle that

t

makes with

l_3

C

which is in the same relative position as the angle at

A

. (iii) Verify that the three angles formed at

A, B,

and

C

on the same side of the transversal constitute an arithmetic progression, showing all steps.