A footbridge crosses two straight roads and

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

Problem

A footbridge

EF

crosses two straight roads

AB

and

CD

. The bridge meets road

AB

at point

E

and road

CD

at point

F

. The angle between the bridge and road

AB

on the upper side of the bridge is

(2y - 5)^\circ

, while the angle between the bridge and road

CD

on the corresponding upper side is

(115 - y)^\circ

. Answer the following questions. (i) Find the value of

y

. (ii) Using your value of

y

, decide whether the two roads

AB

and

CD

are parallel. State complete reasons for your conclusion.