Angles, Angles, Angles

- vshiroky

Angles, Angles, Angles

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- schrodinger

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- vshiroky

|dw:1437636777764:dw|

- vshiroky

Which 2 angles are supplementary?
Which 2 angles are alternate exterior?
Which 2 are congruent?
Which 2 are corresponding?
If angle 2 is 70 degrees, what is the measure of angle 1, 4, 6, 3, and 7?

- vshiroky

This is my daughters homework, I'm just trying to check her answers while studying for my nursing exam lol

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## More answers

- vshiroky

@ganeshie8

- ganeshie8

Is it given that the both horizontal lines shown in the diagram are "parallel" ?

- vshiroky

Yes lol I drew the best I could

- ganeshie8

in geometry we use "arrow" signs to indicate that the lines are parallel
|dw:1437637316997:dw|

- vshiroky

Oh I guess it does have arrows I just didnt know I needed them

- ganeshie8

supplementary angles are the angles that add up to 180
also these are the angles that make a "straight line"

- vshiroky

so 7 and 8 would be complementary?

- ganeshie8

for example, in the given diagram, angles \(1\) and \(2\) are supplementary as they form a straight line :
|dw:1437637475811:dw|

- vshiroky

Ok so it would be any angle like thaT? It gives her options for each one and she chose 7 and 8

- ganeshie8

Yes, the angles \(7\) and \(8\) also form a supplementary pair
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- vshiroky

Great. What does alternate exterior mean?

- vshiroky

Her options were 1 & 3, 2& 6, 4 &7, 7 & 1

- ganeshie8

as the name says,
exterior means outside
alternate means they are on alternate sides

- ganeshie8

I'll show an example for this pair, then it becomes clear

- ganeshie8

lets call the region between the two horizontal lines "interior"
and the region outside as "exterior"
next, notice that the angles \(2\) and \(8\) are "exterior"
and are also on either side of the transversal
so these form an "alternate exterior angles pair"
|dw:1437637704839:dw|

- vshiroky

so 7 & 1 on mine would be

- ganeshie8

Yes!

- vshiroky

Can you tell me what congruent is? her options are 1 & 4, 4 & 5, 1 & 5, 7 & 8

- ganeshie8

"congruent" means "equal"

- vshiroky

1 & 5

- ganeshie8

Here is a theorem :
corresponding angles are congruent when the lines are parallel

- ganeshie8

|dw:1437638008666:dw|

- UsukiDoll

that would mean that if we have parallel lines, then the corresponding angles are congruent (equivalent)?

- UsukiDoll

._. that was the converse of the theorem.

- vshiroky

Ok so 1 & 5 is correct.
Corresponding angels would be 4 & 8... Her options were 4 & 8, 4 & 6, 1 & 2, 2& 8

- ganeshie8

Yes, corresponding angles are "congruent" when lines are parallel
so their measures are "equal"

- ganeshie8

in geometry we generally use "congruent" and "equal" interchangeably

- vshiroky

I'm not the student. This is my daughters homework... I'm just trying to make sure they are right while I study for my nursing exam at the same time lol

- UsukiDoll

@skullpatrol memorizing theorems can be useful...but what if they get parts of it confused with other theorems? There are a bunch of theorems out there and in Euclidean Geometry there is a truckload. emphasis on the word "truckload"

- ganeshie8

|dw:1437638256448:dw|

- vshiroky

If the angle 2 is 70 degrees, the measure of angle 1 is 110 degrees right?

- UsukiDoll

what about 3 and 7 ? do they correspond? @ganeshie8
I'm just asking because I need to refresh my memory .

- ganeshie8

Yes, because 2 and 1 are supplementary angles
so they must add up to 180

- ganeshie8

Yes @UsukiDoll looks there are four pairs of corresponding angles

- vshiroky

Ok awesome... If the measure of angle 2 is 70 degrees, what is the measure of angle 4? it is also 70 right?

- UsukiDoll

70+70 = 140 though ?

- vshiroky

Right but they are both acute angles so it cant be more than 90 degrees

- UsukiDoll

true...

- ganeshie8

angle2 and angle4 are "vertical angles"
vertical angles are always congruent, so yeah you're correct.

- UsukiDoll

vertical angles?

- vshiroky

If angle 2 is 70 degrees what is the measure of angle 6? its 110 right?

- vshiroky

I lied its also 70

- ganeshie8

angles 2 and 6 are corresponding angles
corresponding angles are congruent, so they both equal 70
|dw:1437638650175:dw|

- vshiroky

Ok can I post another one?

- vshiroky

|dw:1437638698030:dw|

- vshiroky

What is the vertical angle of angle 4? she put 2..

- ganeshie8

Nope.

- ganeshie8

|dw:1437638841032:dw|

- vshiroky

So the vertical angel of 7 would be 8

- ganeshie8

Yes

- vshiroky

angle 1 and angle 3 are not congruent right?
and 2 and 7 are also not congruent right?

- ganeshie8

Hey wait, has the diagram changed ?

- vshiroky

Lol yes sorry

- ganeshie8

Okay just making sure

- ganeshie8

angles 2 and 7 are called "alternate interior angles"

- ganeshie8

are the horizontal liens shown parallel this time also ?

- vshiroky

So they aren't congruent?

- vshiroky

yes they are

- ganeshie8

"alternate interior angles" are congruent when lines are parallel

- vshiroky

Her question is are 1 & 3 congruent to eachother and are 2 & 7 congruent to eachother

- ganeshie8

|dw:1437639119061:dw|

- vshiroky

So 2 and 7 are 1 and 3 arent

- ganeshie8

Yes. 2 and 7 are congruent because they form alternate interior angles pair
but there is no reason for 1 and 3 to be congruent.

- vshiroky

Ok great... Just 2 more questions... what do complementary angles add up to? she put 90 degrees..
What do supplementary angles add up to... she put 180

- ganeshie8

Correct. I see she knows some geometry!

- vshiroky

Lol yes thank you for your help!

- ganeshie8

np

- UsukiDoll

@ganeshie8 what happened to your medals? you had 4?

- ganeshie8

hmm idk but here is what system says
{"id":"ganeshie8","detailedMedals":[{"receiver":"ganeshie8","givers":["iambatman","vshiroky","UsukiDoll"],"latestMedal":"Thu, 23 Jul 2015 08:18:40 GMT","update":{"body":"Angles, Angles, Angles ","link":"http://openstudy.com/updates/55b098a6e4b04559507a768c"}}]}

- UsukiDoll

where did you get that?

- ganeshie8

last two numbers `0/1` is the range of questions

- ganeshie8

for example below fetches medals info for questions between 3 and 7
http://openstudy.com/api/v1/users/ganeshie8/medals/3/7

- ganeshie8

questions are sorted based on time

- UsukiDoll

saw it... I've done 100 XD
0 to 100 that's cool

- ganeshie8

Have fun :)

- UsukiDoll

oh I will I did 1700 and got to my first medal ever. XD

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