Question

Draw a map to show the route of Indu and Puspa to their house, school and hospital. The following information is given : (a) From their house, both go straight and walk 5/2 km to reach at the traffic signal. (b) Now both takes a right turn and walk 2 km straight, to reach at a T-point. (c) Now Indu takes a right turn and walk 3/2 km to reach the hospital and Puspa take left turn and walk 2 km to reach her school. After drawing the map, also find the distance between the school and the hospital.

Answer 1

Since AB and CD are given to be parallel lines and t is a transversal.

So, ∠5 = ∠1 = 70o [Corresponding angles are equal]

∠3 = ∠1 = 70o [Vertically opp. Angles]

∠3 + ∠6 = 180o [Co-interior angles on same side]

∴ ∠6 = 180o – ∠3

= 180o – 70o = 110o

∠6 = ∠8 [Vertically opp. Angles]

⇒ ∠8 = 110o

⇒ ∠4 + ∠5 = 180o [Co-interior angles on same side]

∠4 = 180o – 70o = 110o

∠2 = ∠4 = 110o [ Vertically opposite angles]

∠5 = ∠7 [Vertically opposite angles]

So, ∠7 = 70o

∴ ∠2 = 110o, ∠3 = 70o , ∠4 = 110o, ∠5 = 70o, ∠6 = 110o, ∠7 = 70o and ∠8 = 110o.