Question

In the given picture, angle 1 =80 degree and angle 8 = 60 degree. Are the lines l and m parallel?( Write proper reason.)

Answer 1

Answer:

no they are not..if they were parallel then angle 1 = 80° and angle 8=100°

or angle 1=120° and angle 8 would be 60°

Answer 2

Given : ∠1 = 80°  , ∠8 = 60°

To Find : Are the lines l and m parallel

Solution:

Transversal line : A line which passes through two lines in the same plane at two distinct points.

Corresponding  angles : A pair of angles that occupy the same relative position at each intersection by a transversal line  

Co- Interior angles : A pair of angles that are on the same side of the transversal and inside the given lines

Interior alternate angles : A pair of angles on the inner side of each of those two lines but on opposite sides of the transversal  

Exterior alternate angles : A pair of angles on the outer side of each of  those two lines but on opposite sides of the transversal  

Properties of angles formed by transversal line  with two parallel lines :

• Corresponding angles are congruent. ( Equal in Measure)

• Alternate angles are congruent.  ( Interiors & Exterior  both )  

• Co-Interior angles are supplementary. ( adds up to 180°)

Converse is also true for above

∠1 = 80°  , ∠8 = 60°

∠5 + ∠ 8 = 180°  linear pair

=> ∠5 + 60° = 180°

=> ∠5 = 120°

∠1 = 80°  ∠5 = 120°

∠1 ≠ ∠ 5  Hence corresponding angles are not equal

so line l and m are not parallel

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