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. substitution property linear pairs theorem symmetric property?∠1? is complementary to ∠2.?∠1? is supplementary to ∠5. ∠2≅∠4 alternate exterior angles theorem corresponding angles postulate ∠2≅∠5 ∠1 is supplementary to ∠2.?∠2≅∠6? consecutive exterior angles theorem

Explanation:

Step1: Recall corresponding - angles property

If two parallel lines are given, corresponding angles are congruent. Since line a is parallel to line b, we can use the corresponding - angles postulate. One possible pair of corresponding angles could be $\angle2\cong\angle6$. So, for statement 2: $\angle2\cong\angle6$ and the reason is "Corresponding Angles Postulate".

Step2: Use linear - pairs and substitution

We know that $\angle1$ and $\angle2$ are a linear pair (by the nature of angles formed by two intersecting lines). By the Linear Pairs Theorem, $\angle1$ is supplementary to $\angle2$. Also, since $\angle2\cong\angle6$ (from step 1), by the Substitution Property, $\angle1$ is supplementary to $\angle6$. For statement 3, we can state that $\angle1$ is supplementary to $\angle2$ and the reason is "Linear Pairs Theorem".

Answer:

1. $\angle2\cong\angle6$, Corresponding Angles Postulate
2. $\angle1$ is supplementary to $\angle2$, Linear Pairs Theorem