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

  A  Alternate interior angles of parallel lines are congruent

Step-by-step explanation:

The referenced angles (1, A), (3, C) are alternate interior angles, not corresponding or exterior. The symmetric property does not apply. The only answer choice with any applicability is the one shown above. (It is also the right choice.)

Step-by-step explanation:

If you observe the image, the statement that Janet wants to justify is

According to the given graph, these angles are inside parallels because by given, and these angles are at different sides of the transversals and , those position define Alternate Interior Angles, which by theorem  they are congruent.

Therefore, the right reason of such congruence is

A . Alternate interior angles of parallel lines are congruent.

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step-by-step explanation:

b

step-by-step explanation:

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (0, 4) and (x₂, y₂ ) = (3, - 5) ← 2 points on the line

m = = = - 3

with m = - 3 and (a, b) = (3, - 5), then

y - (- 5) = - 3(x - 3), that is

y + 5 = - 3(x - 3) → b