Question

line m is parallel to line l.
Show that angle 1 + angle 2 - angle 3 = 180 degree.
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Answer 1

Note :

• Transversal line : The line which intersects two other lines at two distinct points is called transversal line .

• Supplementary angles : Two angles are said to be supplementary if their sum is 180°.

• Exterior angle property of a triangle : The sum of two interior angles of a triangle is equal to the opposite exterior angle .

Given :

Lines m and n are parallel , ie. m | | n .

To prove :

∠1 + ∠2 - ∠3 = 180°

Proof :

We have ,

m | | n and AE is transversal .

Thus ,

→ ∠1 + ∠E = 180° [ °•° Co-interior angles are supplementary ]

→ ∠E = 180° - ∠1 --------(1)

Also ,

In ∆CDE ,

→ ∠3 + ∠E = ∠2 [ °•° Exterior angle property of a triangle ]

→ ∠E = ∠2 - ∠3 ----------(2)

Form eq-(1) and (2) , we have ;

→ 180° - ∠1 = ∠2 - ∠3

→ 180° = ∠1 + ∠2 - ∠3

→ ∠1 + ∠2 - ∠3 = 180°

Hence proved .