Question

Given: Lines y and z are parallel, and ABC forms a triangle. Prove: m∠5 + m∠2 + m∠6 = 180° Lines y and z are parallel. Triangle A B C sits between the 2 lines with point A on line y and points C and B on line z. Angle C A B is 2. Its exterior angle to the left is 1 and its exterior angle to the right is 3. Angle A B C is 6 and its exterior angle to the right is 7. Angle B C A is 5 and its exterior angle to the left is 4. Statements Reasons 1. ABC is a triangle 1. given 2. y ∥ z 2. given 3. ∠1 ≅ ∠5; ∠3 ≅ ∠6 3. ? 4. m∠1 = m∠5; m∠3 = m∠6 4. def. ≅ 5. m∠1 + m∠2 + m∠3 = m∠LAM 5. ∠ addition postulate 6. m∠1 + m∠2 + m∠3 = 180° 6. def. Straight angle 7. m∠5 + m∠2 + m∠6 = 180° 7. substitution Which could be the missing reason in Step 3? alternate interior angles are congruent alternate exterior angles are congruent vertical angles are congruent corresponding angles are congruent

Answer 1

The answer is A. alternate interior angles are congruent

Explanation:

I tried all my options and that one was correct.

Answer 2

The correct option is;

Alternate interior angles

Explanation:

The m∠5 + m∠2 + m∠6 = 180° proof is given as follows;

Statement
`{}` Reason

1. ABC is a triangle
`{}` Given

2. y ║ z
`{}` Given

3. ∠1 ≅ ∠5; ∠3 ≅ ∠6 Alternate interior angles

4. m∠1 = m∠5; m∠3 = m∠6
`{}` Definition of (congruency) ≅

5. m∠1 + m∠2 + ∠3 = m∠LAM
`{}` ∠Addition postulate

6. m∠1 + m∠2 + ∠3 = 180°
`{}` Definition of straight angles

7. m∠5 + m∠2 + ∠6 = 180°
`{}` Substitution property

Step 3;

Given that line y is parallel to line z, we have that the transversal AB will make equal corresponding angles with the lines y and z, therefore, ∠6 will be equivalent to segment AB extended

Which gives, ∠6 is supplementary to ∠a where ∠a = ∠1 + ∠2

Therefore, given that ∠3 is also supplementary to ∠a where as we have above, ∠a = ∠1 + ∠2, we have that ∠3 = ∠6 and ∠3 ≅ ∠6 where ∠3 and ∠6 are alternate interior angles;

Similarly, ∠1 ≅ ∠5 by alternate interior angles of two parallel lines property.