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.

m5 + m1 = 180

m5 = m3 + m2

Question:

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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

Step-by-step explanation:

Given: line l is parallel to line m

We need prove that the interior angles of a triangle have a sum of 180°. In order to do that, the angles in the triangle = 180°

∠1 + ∠2  + ∠3  = 180°

Alternate angles:

∠1 = ∠4

∠6 = ∠2

∠5 = ∠3 + ∠6

Checking the options and inserting the values above in them:

a) 1 and 4 are alternate interior angles

∠1 = ∠4

This gives one of the side of the interior angles. The alternate angles enables us to find the sum of the interior angles. It is correct

b) m4 + m5 + m6 = 180

∠4 + ∠5 + ∠6 = 180°

∠1 + (∠3 + ∠6) + ∠2 = 180°

The above option wont give ∠1 + ∠2  + ∠3  = 180°. Hence it is wrong.

c) m5 + m1 = 180

(∠3 + ∠6) + ∠1 = 180°

∠5 = (∠3 + ∠6) = ∠3 + ∠2

∠3 + ∠2 + ∠1 = 180°

This option is correct

d) m5 = m3 + m2

∠5 = ∠3 + ∠2

From the diagram, ∠5 + ∠1 = 180° (angles on a straight line)

∠5 = ∠3 + ∠2

This option can be used to get sum of interior angles.

parallelogram is the   answer