Question

In the diagram provided, line l is parallel to line m. Select which of the following statements could be used to prove that the interior angles of a triangle have a sum of 180°. You may choose more than one correct answer.

1 and 4 are alternate interior angles.
m4 + m5 + m6 = 180.
m5 + m1 = 180.
m5 = m3 + m2.

Answer 1

∠5  + ∠1  = 180° can be used  and ∠5 = ∠3 + ∠2 can be used

Step-by-step explanation:

line l is parallel to line m

to prove that the interior angles of a triangle have a sum of 180°

We need to show that

∠1 + ∠2  + ∠3  = 180°

now given

∠4 + ∠5 + ∠6 = 180°

∠4 = ∠1

∠6 = ∠2

but ∠5 =∠6 + ∠3

=> ∠1 + ∠6 + ∠3 + ∠2 = 180°

=> ∠1 + ∠2 + ∠3 + ∠6  = 180°  ( hence this can not be used to prove)

∠5  + ∠1  = 180°

∠5 =∠6 + ∠3

∠6 = ∠2

∠5 =∠2 + ∠3

∠2 + ∠3   + ∠1  = 180°

Hence  ∠5  + ∠1  = 180° can be used

∠5 = ∠3 + ∠2

∠5 + ∠1 = 180° ( Straight line)

=> ∠3 + ∠2 + ∠1 = 180°

Hence ∠5 = ∠3 + ∠2 can be used

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Answer 2

Answer:

The answer will be

m5 + m1 = 180.

m5 = m3 + m2.

Step-by-step explanation: some one already explained it