anonymous
  • anonymous
I have a trapeziod @ the top left is L, top right is M, bottom right is N and the bottom left is K. With 12x + 17 is below the L with -13+ 10x being above the K. For this we need to find the length of the angle indicated. We must find m
Geometry
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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phi
  • phi
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|
phi
  • phi
You now have an algebra problem: the two expressions 12x + 17 and -13+ 10x sum to 180ยบ solve for x. Use that value to find the measure of
anonymous
  • anonymous
|dw:1378134148157:dw| it looks like this, can you teach me how to work it out?

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anonymous
  • anonymous
|dw:1378134384761:dw|
anonymous
  • anonymous
2x=17 am I correct?
phi
  • phi
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?
anonymous
  • anonymous
yes I beleive they are equal
phi
  • phi
I think you are missing something? Do you understand that angle LKN + angle KLM = 180 ?
anonymous
  • anonymous
please explain
phi
  • phi
First fact: a trapezoid has two parallel sides. In your case the parallel lines are LM and KN follow ?
anonymous
  • anonymous
give me a second I'm looking @ my paper
anonymous
  • anonymous
yes I see how LM &KN are parrell
phi
  • phi
econd fact (about two parallel line) see http://www.mathopenref.com/anglestransinterior.html what does that say ?
anonymous
  • anonymous
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|
phi
  • phi
ask again
anonymous
  • anonymous
|dw:1378136770694:dw|
anonymous
  • anonymous
I think x is 15, am I correct?
phi
  • phi
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)
phi
  • phi
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
anonymous
  • anonymous
x=15, how does that look?
anonymous
  • anonymous
now do I take 180 and divide it by 15=12
phi
  • phi
x=15, how does that look? Not good. how did you get that ?
phi
  • phi
-13+ 10x + 12x + 17 = 180 first what is 17 - 13 ?
anonymous
  • anonymous
4 and I took that and added it to 180, then I combined the x's and divided from 184
phi
  • phi
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 ?
anonymous
  • anonymous
I feel like such an idiot the answer is 176
phi
  • phi
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 ?
anonymous
  • anonymous
and I have the x on the left side by itself
anonymous
  • anonymous
leaving me with 22x=176
anonymous
  • anonymous
now do I divide 176 by 22=
phi
  • phi
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
anonymous
  • anonymous
which will leave me with 8
phi
  • phi
Now use x=8 to figure out the angle at K
anonymous
  • anonymous
see that's where i'm having problems
phi
  • phi
angle at K = -13+ 10x replace x with 8 (remember 10x is short for 10 times x)
anonymous
  • anonymous
k=67, but what about 12x+17=
phi
  • phi
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
phi
  • phi
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
anonymous
  • anonymous
for a total of 360?
phi
  • phi
all 4 sided figures have 4 interior angles that add up to 360 degrees
anonymous
  • anonymous
thank-you for your help.
anonymous
  • anonymous
|dw:1378140252301:dw|
anonymous
  • anonymous
Do I do this the same way?

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