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geometry question. the figure will be drawn below ...

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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|dw:1443914739956:dw| In the figure above, if z = 30, what is the value of x + y ?
I thought that it was 150
|dw:1443914836421:dw|

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So \(\angle z\) is an alternate interior angle to both \(\angle x\) and \(\angle y\) therefore \(\angle z = \angle x =\angle y = 30\)
so if z = 30 then wouldn't x equal to 75 or would it be 60?
Okay, let's look at it a different way.
Let's say that in order to complete all the interior angles of a triangle, it has to be = 180, yes?
yes
hints |dw:1443915336204:dw|
Therefore, if we take in to consideration the missing sides, then we will see that (180-y) will make a supplementary angle
and the same goes for x. (180 - x) will give you the other missing angle within the triangle
@jim_thompson5910 so the triangle is not an equilateral triangles?
And then if you add \(\angle z\) + missing side 1 + missing side 2, it would total to 180..
An equilateral triangle means that all sides are 60 degrees.
oh yeah i completely forgot about that
would the answer be 210?
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
`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
210 is correct
thank you!
30 + 360 -x-y = 180 x + y = 30 + 360 - 180 = 210

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