Question

Hello! I have a assignment due soon! If someone can help with transversals of parallel line: solve for x. That would be great! Thank you!

Answer 1

Hello and Good Morning/Afternoon:

Let's take this problem step-by-step:

We know lines 'PQ' and 'RS'

 ==> are parallel to one another

      ==> therefore, corresponding angles formed by the two lines

            intersection with the line 'ON' have the same measure

              for example:

                        ∠PTN = ∠RUT

                        ∠NTQ = ∠TUS

                        ∠PTU = ∠RUO

                        ∠UTQ = ∠OUS

Since ∠PTN = ∠RUT

 ⇒ ∠RUT = 2x + 122

By Vertical Angle Theorem:

 - opposite pairs of angles formed by two intersecting lines are equal in

   measure

           ∠RUT = ∠OUS

      $2x + 122 = 154 - 2x\\2x + 2x + 122 = 154 -2x + 2x\\4x + 122 = 154\\4x + 122-122 = 154-122\\4x = 32\\x = 8$

Answer: 8

Hope that helps!

         

Answer 2

Here is the answer I hope it helped a little bit