Quadrilateral RSTU, diagonals SU and RT intersect at point V.

RSTU is a parallelogram. If m∠TSV = 31° and m∠SVT = 126°, explain how you can find the measure of ∠URV. Show all steps of your work, and refer to any properties of triangles, parallelograms, or triangle congruency theorems as necessary to justify your response.

Question

Quadrilateral RSTU, diagonals SU and RT intersect at point V.

RSTU is a parallelogram. If m∠TSV = 31° and m∠SVT = 126°, explain how you can find the measure of ∠URV. Show all steps of your work, and refer to any properties of triangles, parallelograms, or triangle congruency theorems as necessary to justify your response.

Angle · Answer

Hello @gokrazy223 ! Welcome to QuestionCove!

It is a good idea for questions like these to have a picture of some kind to make the situation clearer

Angle · Answer

I can try drawing it if you don't already have a picture

gokrazy223 · Answer

https://learn.flvs.net/webdav/assessment_images/educator_geometry_v19/02_10_prt2_g4_flvs.png

Angle · Answer

|dw:1613018965772:dw|

Angle · Answer

Unfortunately, because we are not FLVS students, we cannot see the link you just posted - it takes us to an error page

Angle · Answer

ok, so there are many ideas that we can use here

I think the easiest path is if I point out to you that Angle URV and Angle STV are Alternate Interior Angles.

Have you learned about Alternate Interior Angles before?

gokrazy223 · Answer

no thats why i need help

gokrazy223 · Answer

https://us-static.z-dn.net/files/d76/45670b5f9aafe632cfd73397f4dfecab.png

gokrazy223 · Answer

that link has a clear picture

Angle · Answer

Ok then I have updated my picture as well
|dw:1613019244080:dw|

gokrazy223 · Answer

is this the answer or a guide to what i need?

Angle · Answer

Alternate Interior Angles will always be equal to each other

they will look like this kind of pattern

Angle · Answer

|dw:1613019375778:dw|

Angle · Answer

The sum of the interior angles in a triangle add up to 180 degrees

|dw:1613019418369:dw|

Angle · Answer

31 + 126 + x = 180

you can solve for x and get your answer

gokrazy223 · Answer

ill try hold on

gokrazy223 · Answer

x=23

Angle · Answer

there yah go :)

gokrazy223 · Answer

thats the answer fr?

Angle · Answer

yup!

gokrazy223 · Answer

THANK YOU SOO MUCH

gokrazy223 · Answer

what steps will i put in my student box

Angle · Answer

is this a two column proof?

Angle · Answer

I'm asking because some geometry classes want the answer in a specific format

gokrazy223 · Answer

no

Angle · Answer

Angle URV and Angle STV are Alternate Interior Angles
Alternate Interior Angles are equal to each other

Then Angle VST + Angle TVS + Angle STV = 180 degrees because they are the interior angles of a triangle which has a sum of 180

31 + 126 + angle TVS = 180
therefore angle TVS = 23 degrees

gokrazy223 · Answer

will i get a quick response all  the time

Angle · Answer

maybe not all of the time sadly

the helpers on this website are here on a volunteer basis, which is why asking questions is free

gokrazy223 · Answer

thank you soo much for helping

Angle · Answer

you're welcome :)

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