Angles, Angles, Angles

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Angles, Angles, Angles

Mathematics
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|dw:1437636777764:dw|
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?
This is my daughters homework, I'm just trying to check her answers while studying for my nursing exam lol

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Other answers:

Is it given that the both horizontal lines shown in the diagram are "parallel" ?
Yes lol I drew the best I could
in geometry we use "arrow" signs to indicate that the lines are parallel |dw:1437637316997:dw|
Oh I guess it does have arrows I just didnt know I needed them
supplementary angles are the angles that add up to 180 also these are the angles that make a "straight line"
so 7 and 8 would be complementary?
for example, in the given diagram, angles \(1\) and \(2\) are supplementary as they form a straight line : |dw:1437637475811:dw|
Ok so it would be any angle like thaT? It gives her options for each one and she chose 7 and 8
Yes, the angles \(7\) and \(8\) also form a supplementary pair |dw:1437637588173:dw|
Great. What does alternate exterior mean?
Her options were 1 & 3, 2& 6, 4 &7, 7 & 1
as the name says, exterior means outside alternate means they are on alternate sides
I'll show an example for this pair, then it becomes clear
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|
so 7 & 1 on mine would be
Yes!
Can you tell me what congruent is? her options are 1 & 4, 4 & 5, 1 & 5, 7 & 8
"congruent" means "equal"
1 & 5
Here is a theorem : corresponding angles are congruent when the lines are parallel
|dw:1437638008666:dw|
that would mean that if we have parallel lines, then the corresponding angles are congruent (equivalent)?
._. that was the converse of the theorem.
Ok so 1 & 5 is correct. Corresponding angels would be 4 & 8... Her options were 4 & 8, 4 & 6, 1 & 2, 2& 8
Yes, corresponding angles are "congruent" when lines are parallel so their measures are "equal"
in geometry we generally use "congruent" and "equal" interchangeably
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
@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"
|dw:1437638256448:dw|
If the angle 2 is 70 degrees, the measure of angle 1 is 110 degrees right?
what about 3 and 7 ? do they correspond? @ganeshie8 I'm just asking because I need to refresh my memory .
Yes, because 2 and 1 are supplementary angles so they must add up to 180
Yes @UsukiDoll looks there are four pairs of corresponding angles
Ok awesome... If the measure of angle 2 is 70 degrees, what is the measure of angle 4? it is also 70 right?
70+70 = 140 though ?
Right but they are both acute angles so it cant be more than 90 degrees
true...
angle2 and angle4 are "vertical angles" vertical angles are always congruent, so yeah you're correct.
vertical angles?
If angle 2 is 70 degrees what is the measure of angle 6? its 110 right?
I lied its also 70
angles 2 and 6 are corresponding angles corresponding angles are congruent, so they both equal 70 |dw:1437638650175:dw|
Ok can I post another one?
|dw:1437638698030:dw|
What is the vertical angle of angle 4? she put 2..
Nope.
|dw:1437638841032:dw|
So the vertical angel of 7 would be 8
Yes
angle 1 and angle 3 are not congruent right? and 2 and 7 are also not congruent right?
Hey wait, has the diagram changed ?
Lol yes sorry
Okay just making sure
angles 2 and 7 are called "alternate interior angles"
are the horizontal liens shown parallel this time also ?
So they aren't congruent?
yes they are
"alternate interior angles" are congruent when lines are parallel
Her question is are 1 & 3 congruent to eachother and are 2 & 7 congruent to eachother
|dw:1437639119061:dw|
So 2 and 7 are 1 and 3 arent
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.
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
Correct. I see she knows some geometry!
Lol yes thank you for your help!
np
@ganeshie8 what happened to your medals? you had 4?
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"}}]}
where did you get that?
last two numbers `0/1` is the range of questions
for example below fetches medals info for questions between 3 and 7 http://openstudy.com/api/v1/users/ganeshie8/medals/3/7
questions are sorted based on time
saw it... I've done 100 XD 0 to 100 that's cool
Have fun :)
oh I will I did 1700 and got to my first medal ever. XD

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