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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 4 solutions by MathLover1, mananth, ikleyn, n2:
Answer by MathLover1(20854)   (Show Source):
Answer by mananth(16949)  (Show Source):
Answer by ikleyn(53619)  (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.
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About parallel lines and associated angles see the lesson
- Parallel lines
in this site.
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* * * @MathLover1 re-wrote/fixed her solution after reading my post. * * *
Answer by n2(54)  (Show Source):
You can put this solution on YOUR website! .
The alternate interior angles, formed by two parallel lines and a transverse line,
are congruent and have the same measure.
So, we write
2x = x + 30
and obtain immediately from this equation
2x - x = 30,
x = 30 degrees. <<<---=== ANSWER
Solved.
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