street word problem

Question

Main Street and 2nd Street run parallel to each other. Both are one-way streets. Main Street runs north, and 2nd Street runs south. The city is planning to build a new road, also one-way, that runs toward the southeast and cuts through both streets at an angle. Traffic turning off of Main Street would have to make a 125 degree turn onto the new road. What angle would traffic turning off of 2nd Street have to make turning onto the new road?

Answer 1

Main street (one-way North) and 2nd Street (one-way South) are parallel.  A picture often helps:

 

  ∧ 

  |          2nd

  |x         |

  |\         |

  |  \       |

  |    \     |

  |      \   |

  |        \ |

Main      |

              |\

              |y\

              |    \

              V      \

                       ⌋

 

The new road is one-way South-East.  Traffic turning from 2nd street onto the new road must turn slightly to their left the angle y (from travelling South to travelling South-East;  note: all streets are one way).

 

Main Street and 2nd Street are parallel.  So, the angle y is equal to the supplementary angle of angle x (these two angles are alternate interior angles of parallel lines).  Angle y is:    180° – 125° = 55°.

 

Traffic must turn to their left 55°.

Answer 2

Anna,

↑

| X            2

| \             |

|   \           |

|     \         |

|       \       |

|         \     |

|           \   |

M            \ |

             Y  ↓

 

The vertical line with the M at the bottom is Main Street running north.  The line parallel to it, running south is 2nd Street.

 

The diagonal line is the new road and runs SE, i.e. from the top left to the bottom right.

 

X in the diagram is the 125° angle representing the turn that vehicles turning right from Main street onto the new road will have to make.

 

Y is the angle that cars turning from the new road onto 2nd Street will have to make.

 

Since the two street are parallel, the new road is a transversal.  Angles x and y are alternate interior angles and therefore y = 125°

 

Hoping my diagram is clear.