Question

geometry question.

the figure will be drawn below ...

Answer 1

In the figure above, if z = 30, what is the value of x + y ?

Answer 2

I thought that it was 150

Answer 3

So \(\angle z\) is an alternate interior angle to both \(\angle x\) and \(\angle y\) therefore \(\angle z = \angle x =\angle y = 30\)

Answer 4

so if z = 30 then wouldn't x equal to 75 or would it be 60?

Answer 5

Okay, let's look at it a different way.

Answer 6

Let's say that in order to complete all the interior angles of a triangle, it has to be = 180, yes?

Answer 7

yes

Answer 8

hints

Answer 9

Therefore, if we take in to consideration the missing sides, then we will see that (180-y) will make a supplementary angle

Answer 10

and the same goes for x. (180 - x) will give you the other missing angle within the triangle

Answer 11

@jim_thompson5910 so the triangle is not an equilateral triangles?

Answer 12

And then if you add \(\angle z\) + missing side 1 + missing side 2, it would total to 180..

Answer 13

An equilateral triangle means that all sides are 60 degrees.

Answer 14

oh yeah i completely forgot about that

Answer 15

would the answer be 210?

Answer 16

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

Answer 17

`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

Answer 18

210 is correct

Answer 19

thank you!

Answer 20

30 + 360 -x-y = 180

x + y = 30 + 360 - 180 = 210