Parallel Lines & Transversals - Pre Algebra

1. Alternate exterior angles formed by parallel lines and a transversal measure $(3b + 20)^\circ$ and $(b + 60)^\circ$. What is $b$?

   $b = 20$. They are equal, so $3b + 20 = b + 60$ gives $2b = 40$.

2. When two parallel lines are cut by a transversal, how are same-side interior angles related?

   They are supplementary: their measures add to $180^\circ$.

3. A transversal cuts two lines and forms congruent alternate interior angles. What can you conclude about the two lines?

   The lines are parallel (the converse of the alternate interior angles theorem).

4. What is the sum of the two angles in a linear pair?

   $180^\circ$. They form a straight line, so they are supplementary.

5. When two parallel lines are cut by a transversal, how are alternate interior angles related?

   They are congruent. They lie between the parallel lines on opposite sides of the transversal.

6. When two parallel lines are cut by a transversal, how are corresponding angles related?

   They are congruent (equal in measure).

7. Same-side interior angles formed by parallel lines and a transversal measure $(2x)^\circ$ and $(x + 30)^\circ$. What is $x$?

   $x = 50$. They add to $180^\circ$, so $3x + 30 = 180$.

8. Two parallel lines are cut by a transversal. One angle measures $115^\circ$. What is the measure of its alternate interior angle?

   $115^\circ$, because alternate interior angles are congruent.

9. When two parallel lines are cut by a transversal, how are alternate exterior angles related?

   They are congruent. They lie outside the parallel lines on opposite sides of the transversal.

10. Corresponding angles formed by parallel lines and a transversal measure $(5a + 10)^\circ$ and $(7a - 30)^\circ$. What is $a$?

    $a = 20$. Corresponding angles are equal, so $5a + 10 = 7a - 30$ gives $2a = 40$.

11. Two parallel lines are cut by a transversal. One angle measures $72^\circ$. What is the measure of its same-side interior angle?

    $108^\circ$, since same-side interior angles add to $180^\circ$.

12. How are vertical angles related?

    They are congruent. Vertical angles are the opposite angles formed by two intersecting lines.

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