Question

statements reasons 1. line a is parallel to line b. 1. given 2. 2. 3. 3. corresponding angles postulate 4. ∠1 is supplementary to ∠6. 4. ∠1 is supplementary to ∠2. linear pairs theorem?∠2≅∠6? substitution property symmetric property?∠1? is complementary to ∠2?∠1? is supplementary to ∠5. ∠2≅∠4 alternate exterior angles theorem consecutive exterior angles theorem corresponding angles postulate ∠2≅∠5

Explanation:

Step1: Identify a pair of corresponding - angles

$\angle2\cong\angle6$

Step2: State the reason for the corresponding - angles

Corresponding Angles Postulate

Step3: Use the linear - pair relationship

$\angle1$ and $\angle2$ form a linear pair, so $\angle1$ is supplementary to $\angle2$ (Linear Pairs Theorem)

Step4: Use substitution

Since $\angle2\cong\angle6$, by substitution property, $\angle1$ is supplementary to $\angle6$

Answer:

1. $\angle2\cong\angle6$; 2. Given (to match with the Corresponding Angles Postulate in step 3); 4. Substitution Property (because $\angle1$ is supplementary to $\angle2$ and $\angle2\cong\angle6$)