Question

Janet is trying to prove that the sum of the measures of the interior angles of a triangle is 180°.
Which reason can she use to justify the statement in line 6?
A
Alternate interior angles of parallel lines are congruent

B
Corresponding angles of parallel lines are congruent

C
Exterior Angle Theorem

D
Symmetric Property

Answer 1

Alternate interior angles of parallel lines are congruent can be used ti justify that the sum of the measures of the interior angles of a triangle is 180°

Step-by-step explanation:

Alternate interior angles of parallel lines are congruent

Let say ABC is traingle

then Draw a line parallel to BC passing through A , let say MN

Now as per Alternate interior angles of parallel lines are congruent

∠ BAM = ∠ABC

∠CAN = ∠ACB

MN is a Straight line hence

∠ BAM + ∠BAC +∠CAN  = 180°

=> ∠ABC + ∠BAC + ∠ACB = 180°

Sum of angles of triangle = 180°

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