Answer:
1 and 4 are alternate interior angles.
m5 + m1 = 180
m5 = m3 + m2
Question:
The complete version of your question as found in other site is stated below:
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
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.