calculusxy
  • calculusxy
geometry question. the figure will be drawn below ...
Mathematics
  • Stacey Warren - Expert brainly.com
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katieb
  • katieb
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calculusxy
  • calculusxy
|dw:1443914739956:dw| In the figure above, if z = 30, what is the value of x + y ?
calculusxy
  • calculusxy
I thought that it was 150
Jhannybean
  • Jhannybean
|dw:1443914836421:dw|

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Jhannybean
  • Jhannybean
So \(\angle z\) is an alternate interior angle to both \(\angle x\) and \(\angle y\) therefore \(\angle z = \angle x =\angle y = 30\)
calculusxy
  • calculusxy
so if z = 30 then wouldn't x equal to 75 or would it be 60?
Jhannybean
  • Jhannybean
Okay, let's look at it a different way.
Jhannybean
  • Jhannybean
Let's say that in order to complete all the interior angles of a triangle, it has to be = 180, yes?
calculusxy
  • calculusxy
yes
jim_thompson5910
  • jim_thompson5910
hints |dw:1443915336204:dw|
Jhannybean
  • Jhannybean
Therefore, if we take in to consideration the missing sides, then we will see that (180-y) will make a supplementary angle
Jhannybean
  • Jhannybean
and the same goes for x. (180 - x) will give you the other missing angle within the triangle
calculusxy
  • calculusxy
@jim_thompson5910 so the triangle is not an equilateral triangles?
Jhannybean
  • Jhannybean
And then if you add \(\angle z\) + missing side 1 + missing side 2, it would total to 180..
Jhannybean
  • Jhannybean
An equilateral triangle means that all sides are 60 degrees.
calculusxy
  • calculusxy
oh yeah i completely forgot about that
calculusxy
  • calculusxy
would the answer be 210?
Jhannybean
  • Jhannybean
missing side 1 = 180 - x missing side 2 = 180 - y we have z. z+ missing side 1 + missing side 2 = 180 z + (180 - x) + (180 - y) = 180
jim_thompson5910
  • jim_thompson5910
`so the triangle is not an equilateral triangles?` it's not guaranteed it's equilateral, so it's hard to say if yes or no
Zarkon
  • Zarkon
210 is correct
calculusxy
  • calculusxy
thank you!
Jhannybean
  • Jhannybean
30 + 360 -x-y = 180 x + y = 30 + 360 - 180 = 210

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