SOLUTION: Here’s the last question I need help on. Thank you for anyone who solved this!! If angle a and angle b are alternate interior angles solve for X given: A = 2x and B = x

Algebra ->  Angles -> SOLUTION: Here’s the last question I need help on. Thank you for anyone who solved this!! If angle a and angle b are alternate interior angles solve for X given: A = 2x and B = x      Log On


   

Question 1179538: Here’s the last question I need help on. Thank you for anyone who solved this!!

If angle a and angle b are alternate interior angles solve for X given:
A = 2x and B = x+ 30


Found 3 solutions by MathLover1, mananth, ikleyn:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

alternate interior angles are congruent
given:
< a=2x
< b=+x%2B+30
< a=< b
2x=x%2B30
2x-x=30
x=30
< a=2%2A30 => < a=60°
< b=+30%2B+30 => < b=+60°


Answer by mananth(16946) About Me  (Show Source):
Answer by ikleyn(52914) About Me  (Show Source):
You can put this solution on YOUR website!
.


            From the solution by  @MathLover1,  it is clearly seen that
            she  DOES  NOT  KNOW  basic terms,  notions and definitions of  Geometry

            Her solution has nothing in common with the truth.

            I came to bring a correct solution.



Let me start from the proper definition 


    +-------------------------------------------------------------------------+
    |   Alternate interior angles are angles formed when two parallel         |
    |   are intersected by a transversal.                                     | 
    |   The angles are positioned at the inner corners of the intersections   |
    |   and lie on opposite sides of the transversal.                         |
    +-------------------------------------------------------------------------+



One of the first theorem of Geometry states that alternate interior angles at two parallel lines are CONGRUENT, 
i.e. have equal angular measure.


It means that  A = B,   or


    2x = x + 30.


From this equation


    x = 30 degrees.


So, both angles A and B have equal measure of 2*30 = 60 degrees = 30+30 degrees.    ANSWER

Solved.

----------------

About parallel lines and associated angles see the lesson
    - Parallel lines
in this site.


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@MathLover1 re-wrote her solution after reading my post.