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First, you need the definition of a trapezoid A quadrilateral which has at least one pair of parallel sides See http://www.mathopenref.com/trapezoid.html In your case, the top (line LM) and the base (line KN) are parallel You need to know about two parallel lines cut by a transversal See http://www.mathopenref.com/anglestransinterior.html Your problem is, after stripping away the irrelevant detail, |dw:1378130757413:dw|
You now have an algebra problem: the two expressions 12x + 17 and -13+ 10x sum to 180º solve for x. Use that value to find the measure of
|dw:1378134148157:dw| it looks like this, can you teach me how to work it out?
2x=17 am I correct?
I assume the marks on legs LK and MN mean they have equal length? Also, LM is parallel to KN, you can treat leg LK as a transversal from http://www.mathopenref.com/anglestransinterior.html you should see that the interior angles of a transversal add up to 180 can you set up an equation?
yes I beleive they are equal
I think you are missing something? Do you understand that angle LKN + angle KLM = 180 ?
First fact: a trapezoid has two parallel sides. In your case the parallel lines are LM and KN follow ?
give me a second I'm looking @ my paper
yes I see how LM &KN are parrell
econd fact (about two parallel line) see http://www.mathopenref.com/anglestransinterior.html what does that say ?
So what they are|saying the 2 sides are parallel? What are the 2 little line in the middle of the parallel lines? dw:1378136092982:dw|
I think x is 15, am I correct?
they mean that side LK has the same length as side MN but you do not need that info to solve this problem. You need to know that angle LKN + angle KLM = 180 do you understand ? The reason the angles add up to 180 degrees is because they are interior angles of a transversal (side LK ) that crosses two parallel lines (lines KN and LM)
angle LKN + angle KLM = 180 They tell you angle KLM = 12x + 17 angle LKN= -13+ 10x that means we can replace angle LKN with -13+ 10x -13+ 10x + angle KLM = 180 and replace angle KLM with 12x + 17 -13+ 10x + 12x + 17 = 180 now simplify and solve for x
x=15, how does that look?
now do I take 180 and divide it by 15=12
x=15, how does that look? Not good. how did you get that ?
-13+ 10x + 12x + 17 = 180 first what is 17 - 13 ?
4 and I took that and added it to 180, then I combined the x's and divided from 184
ok, 17-13 = 4, so you now have 10x + 12x + 4 = 180 now add -4 to both sides, like this 10x + 12x + 4 -4 = 180-4 simplify, what do you get ?
I feel like such an idiot the answer is 176
on the right side. on the left side you get 10x+12x so you now have 10x + 12x = 176 on the left side you have 10 x's and add 12 more x's. How many x's do you have ?
and I have the x on the left side by itself
leaving me with 22x=176
now do I divide 176 by 22=
10x + 12x + 4 -4 = 176 on the left side 4-4 is 0 so you get 10x + 12x + 0 = 176 but adding 0 can be ignored so it is 10x+12x = 176 22x = 176 divide both sides by 22 on the left 22/22 is 1, and you get 1*x or just x on the right you get 176/22 =8 So you now have x=8
which will leave me with 8
Now use x=8 to figure out the angle at K
see that's where i'm having problems
angle at K = -13+ 10x replace x with 8 (remember 10x is short for 10 times x)
k=67, but what about 12x+17=
12x+17 is the angle at L do you need to find it? you can find it two different ways. 1) replace x with 8 in 12*x+17 to get 12*8+17= 96+17= 113 2) you know angle K + angle L = 180. angle K=67, so you have 67+ L = 180 L = 180-67 = 113 so angle L is 113 degrees
You have an isosceles trapezoid (because leg LK = leg MN) see http://www.mathwarehouse.com/geometry/quadrilaterals/isosceles-trapezoid.php what that means is angle K = angle N and angle L = angle M
for a total of 360?
all 4 sided figures have 4 interior angles that add up to 360 degrees
thank-you for your help.
Do I do this the same way?