Guided Practice

Practice Problem #1

What must x equal for these lines to be parallel?

Line x is above line y and they are a pair of horizontal lines that are cut by a transversal. The angle to the upper left of the intersection with line y is 100 degrees. The angle to the bottom right of the intersection with line x has value x minus 15

Let's start by identifying the relationship between these angles.

  • alternate interior
  • corresponding
  • same side interior
  • vertical
  • alternate exterior
  • linear pair
  • same side exterior

Answer: alternate interior

Ok, we know these are alternate interior angles. What is the relationship between these angles?

  • congruent
  • complementary
  • supplementary

Answer: congruent

Correct! Alternate interior angles are congruent. Which equation should we use to solve for x?

  • x - 15 + 100 = 90
  • x - 15 = 100
  • x - 15 + 100 = 180

Answer: x - 15 = 100

Correct! Now we just solve.

x - 15 = 100

x = ___

Answer: 115

Video example.

Practice Problem #2

What must x equal for these lines to be parallel?

Line x is above line y and they are a pair of horizontal lines that are cut by a transversal. The angle to the bottom left of the intersection with line x has value x + 5. The angle to the bottom left of the intersection with line y has value 75

Let's start by identifying the relationship between these angles.

  • alternate interior
  • corresponding
  • same side interior
  • vertical
  • alternate exterior
  • linear pair
  • same side exterior

Answer: same side interior

Ok, we know these are same side interior angles. What is the relationship between these angles?

  • congruent
  • complementary
  • supplementary

Answer: supplementary

Correct! Same side interior angles are congruent. Which equation should we use to solve for x?

  • x + 5 + 75 = 90
  • x + 5 = 75
  • x + 5 + 75 = 180

Answer: x + 5 + 75 = 180

Great! Now, just solve.

x + 5 + 75 = 180

x + ___ = 180

Answer: 80

x = ___

Answer: 100

Video example.

Practice Problem #3

What must x equal for these lines to be parallel?

Line x is above line y and they are a pair of horizontal lines that are cut by a transversal. The angle to the upper left of the intersection with line x has value 2x. The angle to the upper left of the intersection with line y has value 80

Let's start by identifying the relationship between these angles.

  • alternate interior
  • corresponding
  • same side interior
  • vertical
  • alternate exterior
  • linear pair
  • same side exterior

Answer: corresponding

Ok, we know these are corresponding angles. What is the relationship between these angles?

  • congruent
  • complementary
  • supplementary

Answer: congruent

Correct! Corresponding angles are congruent. Which equation should we use to solve for x?

  • 2x + 80 = 90
  • 2x = 80
  • 2x + 80 = 180

Answer: x + 5 + 75 = 180

Now, just solve.

2x = 80

x = ___

Answer: 40

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