Exercise 31 Page 326

Let's see what information is given on the diagram.

• Oak street is a transversal of the other two streets, so angles ∠ 1 and ∠ 2 are consecutive interior angles.
• Notice that there are markers on the lines representing Elm and Plums street. These markers mean that these two streets are parallel.

  Since Elm and Plum streets are parallel, we can use the Consecutive Interior Angles Theorem to conclude that angles ∠ 1 and ∠ 2 are supplementary.

  
  Using that the measures of supplementary angles add to 180, this will let us find x.
  m∠ 1+m∠ 2=180

  SubstituteII

  m∠ 1= 55, m∠ 2= x

  55+ x=180

  SubEqn

  LHS-55=RHS-55

  x=125
  The value of x on the diagram is 125.