The rectangle shown is enlarged such that each side is multiplied by the value of the width, 2x. Which expression represents the
1 answer:
You might be interested in
Answer:
The correct option is;
Alternate interior angles
Step-by-step 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.
