SOLUTION: There is a triangle, with the outer side which equals (3x-18). They give you one remote interior angle which is 30. They want you to find the restrictions on x. I found the answ

Algebra ->  Algebra  -> Angles -> SOLUTION: There is a triangle, with the outer side which equals (3x-18). They give you one remote interior angle which is 30. They want you to find the restrictions on x. I found the answ      Log On

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Question 22618: There is a triangle, with the outer side which equals (3x-18). They give you one remote interior angle which is 30. They want you to find the restrictions on x. I found the answer, but i just couldn't understand how to get it. The answer was 16
Answer by eclecticist(12) About Me  (Show Source):
You can put this solution on YOUR website!
If you've learned about the theorem that states that any exterior angle of a triangle is greater than any of the 2 remote interior angles, then you can solve this problem. Since you know that the exterior angle has to be greater than the interior angle, you can set up this inequality
3x - 18 > 30
3x > 48
x > 16
However, you also know that the exterior angle can't be 180, or there would be no triangle, but a line. Now you can set up a second inequality.
3x - 18 < 180
3x < 198
x < 66
By combining these two inequalities you obtain the solution, 16 < x < 66