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

4 + 5 7/9= 9 7/9

step-by-step explanation:

(x3 + 6x2 + 2x - 6) • (x - 1)

step-by-step explanation:

polynomial long division :

3.2     polynomial long division

dividing :   x4+5x3-4x2-8x+6

                              ("dividend")

by         :     x-1     ("divisor")

dividend     x4   +   5x3   -   4x2   -   8x   +   6

- divisor   * x3     x4   -   x3            

remainder         6x3   -   4x2   -   8x   +   6

- divisor   * 6x2         6x3   -   6x2        

remainder             2x2   -   8x   +   6

- divisor   * 2x1             2x2   -   2x    

remainder               -   6x   +   6

- divisor   * -6x0               -   6x   +   6

remainder                     0

quotient :   x3+6x2+2x-6   remainder:   0

option 3 . (5x + 1) - (-10x + 6)

step-by-step explanation:

option 1 :

(4x + 3) + (-9x + 4)

or 4x+3 -9x + 4

or -5x + 7

option 2

(x - 2) - (6x - 9)

or x-2-6x + 9

or -5x + 7

option 3

(5x+ + 6)

or 5x + 1 + 10x -6

or 15x -5

option 4

-4x+2x+7-3x

-7x + 2x + 7

-5x + 7

hence only option 3 did   not satisfy the given simplify expression.