Using trapezoid PQRS, solve for x
How do I work this without getting a negative? my multiple choice is:
38
16
34
27
the way I did the problem is:
3x+17=2x-7
-2x -2x
x+17=-7
-17 -17
x=-24
That is not a multiple choice answer... did I do something wrong?

Question

Using trapezoid PQRS, solve for x
How do I work this without getting a negative? my multiple choice is:
38
16
34
27
the way I did the problem is:
3x+17=2x-7
-2x        -2x
x+17=-7
   -17   -17
x=-24 
That is not a multiple choice answer... did I do something wrong?

anonymous · Answer

attachment

hero · Answer

Uh...the angle can't be negative can it?

anonymous · Answer

no but how do you figure that out without it becoming a negative did I do the process wrong?

hero · Answer

There's a property of trapezoids that involve consecutive angles. Are you aware of what it is?

anonymous · Answer

ummm No?

hero · Answer

Perhaps the hardest property to spot is the one about supplementary angles. Because of the parallel sides PQ and RS, consecutive angles are same-side interior angles and are thus supplementary.

hero · Answer

Supplementary, meaning, the angles add to 180 degrees.

anonymous · Answer

so the angles have to equal 180?

hero · Answer

Yes

anonymous · Answer

well how does that work when you have to find the ange for x?

hero · Answer

(3x+17)+(2x-7) = 180

anonymous · Answer

OHHH i didnt know I could do it like that

anonymous · Answer

can you show me how to do it like that?

hero · Answer

(3x+17)+(2x-7) = 180
3x + 2x + 17 - 7 = 180
5x + 10 = 180
5x = 170
  x = 34

Check: 
3x + 17
3(34) + 17 = 119

2x - 7 
2(34) -7 = 61

119 + 61 = 180

hero · Answer

Just to emphasize, x = 34