vshiroky
  • vshiroky
Angles, Angles, Angles
Mathematics
  • Stacey Warren - Expert brainly.com
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jamiebookeater
  • jamiebookeater
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vshiroky
  • vshiroky
|dw:1437636777764:dw|
vshiroky
  • 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
  • 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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vshiroky
  • vshiroky
@ganeshie8
ganeshie8
  • ganeshie8
Is it given that the both horizontal lines shown in the diagram are "parallel" ?
vshiroky
  • vshiroky
Yes lol I drew the best I could
ganeshie8
  • ganeshie8
in geometry we use "arrow" signs to indicate that the lines are parallel |dw:1437637316997:dw|
vshiroky
  • vshiroky
Oh I guess it does have arrows I just didnt know I needed them
ganeshie8
  • ganeshie8
supplementary angles are the angles that add up to 180 also these are the angles that make a "straight line"
vshiroky
  • vshiroky
so 7 and 8 would be complementary?
ganeshie8
  • ganeshie8
for example, in the given diagram, angles \(1\) and \(2\) are supplementary as they form a straight line : |dw:1437637475811:dw|
vshiroky
  • vshiroky
Ok so it would be any angle like thaT? It gives her options for each one and she chose 7 and 8
ganeshie8
  • ganeshie8
Yes, the angles \(7\) and \(8\) also form a supplementary pair |dw:1437637588173:dw|
vshiroky
  • vshiroky
Great. What does alternate exterior mean?
vshiroky
  • vshiroky
Her options were 1 & 3, 2& 6, 4 &7, 7 & 1
ganeshie8
  • ganeshie8
as the name says, exterior means outside alternate means they are on alternate sides
ganeshie8
  • ganeshie8
I'll show an example for this pair, then it becomes clear
ganeshie8
  • 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
  • vshiroky
so 7 & 1 on mine would be
ganeshie8
  • ganeshie8
Yes!
vshiroky
  • vshiroky
Can you tell me what congruent is? her options are 1 & 4, 4 & 5, 1 & 5, 7 & 8
ganeshie8
  • ganeshie8
"congruent" means "equal"
vshiroky
  • vshiroky
1 & 5
ganeshie8
  • ganeshie8
Here is a theorem : corresponding angles are congruent when the lines are parallel
ganeshie8
  • ganeshie8
|dw:1437638008666:dw|
UsukiDoll
  • UsukiDoll
that would mean that if we have parallel lines, then the corresponding angles are congruent (equivalent)?
UsukiDoll
  • UsukiDoll
._. that was the converse of the theorem.
vshiroky
  • 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
  • ganeshie8
Yes, corresponding angles are "congruent" when lines are parallel so their measures are "equal"
ganeshie8
  • ganeshie8
in geometry we generally use "congruent" and "equal" interchangeably
vshiroky
  • 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
  • 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
  • ganeshie8
|dw:1437638256448:dw|
vshiroky
  • vshiroky
If the angle 2 is 70 degrees, the measure of angle 1 is 110 degrees right?
UsukiDoll
  • UsukiDoll
what about 3 and 7 ? do they correspond? @ganeshie8 I'm just asking because I need to refresh my memory .
ganeshie8
  • ganeshie8
Yes, because 2 and 1 are supplementary angles so they must add up to 180
ganeshie8
  • ganeshie8
Yes @UsukiDoll looks there are four pairs of corresponding angles
vshiroky
  • 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
  • UsukiDoll
70+70 = 140 though ?
vshiroky
  • vshiroky
Right but they are both acute angles so it cant be more than 90 degrees
UsukiDoll
  • UsukiDoll
true...
ganeshie8
  • ganeshie8
angle2 and angle4 are "vertical angles" vertical angles are always congruent, so yeah you're correct.
UsukiDoll
  • UsukiDoll
vertical angles?
vshiroky
  • vshiroky
If angle 2 is 70 degrees what is the measure of angle 6? its 110 right?
vshiroky
  • vshiroky
I lied its also 70
ganeshie8
  • ganeshie8
angles 2 and 6 are corresponding angles corresponding angles are congruent, so they both equal 70 |dw:1437638650175:dw|
vshiroky
  • vshiroky
Ok can I post another one?
vshiroky
  • vshiroky
|dw:1437638698030:dw|
vshiroky
  • vshiroky
What is the vertical angle of angle 4? she put 2..
ganeshie8
  • ganeshie8
Nope.
ganeshie8
  • ganeshie8
|dw:1437638841032:dw|
vshiroky
  • vshiroky
So the vertical angel of 7 would be 8
ganeshie8
  • ganeshie8
Yes
vshiroky
  • vshiroky
angle 1 and angle 3 are not congruent right? and 2 and 7 are also not congruent right?
ganeshie8
  • ganeshie8
Hey wait, has the diagram changed ?
vshiroky
  • vshiroky
Lol yes sorry
ganeshie8
  • ganeshie8
Okay just making sure
ganeshie8
  • ganeshie8
angles 2 and 7 are called "alternate interior angles"
ganeshie8
  • ganeshie8
are the horizontal liens shown parallel this time also ?
vshiroky
  • vshiroky
So they aren't congruent?
vshiroky
  • vshiroky
yes they are
ganeshie8
  • ganeshie8
"alternate interior angles" are congruent when lines are parallel
vshiroky
  • vshiroky
Her question is are 1 & 3 congruent to eachother and are 2 & 7 congruent to eachother
ganeshie8
  • ganeshie8
|dw:1437639119061:dw|
vshiroky
  • vshiroky
So 2 and 7 are 1 and 3 arent
ganeshie8
  • 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
  • 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
  • ganeshie8
Correct. I see she knows some geometry!
vshiroky
  • vshiroky
Lol yes thank you for your help!
ganeshie8
  • ganeshie8
np
UsukiDoll
  • UsukiDoll
@ganeshie8 what happened to your medals? you had 4?
ganeshie8
  • 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
  • UsukiDoll
where did you get that?
ganeshie8
  • ganeshie8
last two numbers `0/1` is the range of questions
ganeshie8
  • ganeshie8
for example below fetches medals info for questions between 3 and 7 http://openstudy.com/api/v1/users/ganeshie8/medals/3/7
ganeshie8
  • ganeshie8
questions are sorted based on time
UsukiDoll
  • UsukiDoll
saw it... I've done 100 XD 0 to 100 that's cool
ganeshie8
  • ganeshie8
Have fun :)
UsukiDoll
  • UsukiDoll
oh I will I did 1700 and got to my first medal ever. XD

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