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.
Answers
∠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:
The answer will be
m5 + m1 = 180.
m5 = m3 + m2.
Step-by-step explanation: some one already explained it