# Find all angles

#### happiness

##### Junior Member
Can't understand the top or bottom one. Can someone help me find the angles? I have no clue.

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#### yma16

##### Junior Member
1+2=180-70-30-29=51
3=180-1-2=129

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#### happiness

##### Junior Member
1+2=180-70-30-29=51
3=180-1-2=129
Thanks, how did you get those numbers?

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#### tkhunny

##### Moderator
Staff member
Why were you given this problem? Homework? Friend?

If it were fair for you to have been given this problem, you would have been given sufficient information about triangles.

Can you tell me what an "Interior Angle" of a triangle is? You'll need to know that.
Do these internal angles have anu special properties? You'll have to know at least one.

Do some read and then tell us where those numbers came from. Here's a place where you can start. https://www.mathopenref.com/triangleinternalangles.html

#### yma16

##### Junior Member
Looks like "1, 2, 3" means angle#1, angle#2, angle#3 ??????

S'gotta be the weirdest post I've seen
they are, as in the picture. I could only figure out 3.

I do not think there is enough info for others.

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#### stapel

##### Super Moderator
Staff member
Can't understand the top or bottom one. Can someone help me find the angles? I have no clue.
What do you mean by "can't understand" the two exercises? (I'm assuming the "ones" are exercises related to the two drawn figures.) To what "angles" are you making reference? When you say you "have no clue", does this mean that you're trying to "study" for a placement test, but haven't actually ever taken geometry, so you don't understand what the exercises mean?

For the first exercise, the drawing appears to be something along the lines of the following:

Code:
lines:

6x+18      /
g ------ ----/----
10y+2    /
/
3x+9y  /
h -------/--------
/
I am assuming that "g" and "h" are names for the two horizontal-ish lines. Is this correct? If so, are these lines meant to be parallel? If not, for what do "g" and "h" stand? Is the slanty line meant to be a transversal, or does it stand for something else? I'd thought that "6x + 18" and "10y + 2" weren't meant to be a fraction -- but the line between them does not appear to be connected to the rest of that horizontal-ish line, so maybe they are a fraction? Either way, for what do these expressions stand? How does "3x + 9y" relate? What are the instructions? Your subject line says to "find all angles", but no angles are labelled, which makes it kinda hard to know if you've arrived at the correct values (when checking in the back of the book).

For what I'm assuming is the second exercise, you have a drawing that looks kind of like this:

Code:
nested triangles:

/\
/70\
/    \
/      \
/        \
/          \
/     ..     \
/30  .' 3'.  29\
/  .'        '.  \
/.' 1          2 '.\
*--------------------*
Unfortunately, since no other information is provided (such as whether the outer triangle is isosceles; if "1", "2", and "3" are numbers of angles, or if they're [what I'm assuming are] angle measures, like "70", "30", and "29"), it would not appear that this question in answerable. Sorry.

#### happiness

##### Junior Member
What do you mean by "can't understand" the two exercises? (I'm assuming the "ones" are exercises related to the two drawn figures.) To what "angles" are you making reference? When you say you "have no clue", does this mean that you're trying to "study" for a placement test, but haven't actually ever taken geometry, so you don't understand what the exercises mean?

For the first exercise, the drawing appears to be something along the lines of the following:

Code:
lines:

6x+18      /
g ------ ----/----
10y+2    /
/
3x+9y  /
h -------/--------
/
I am assuming that "g" and "h" are names for the two horizontal-ish lines. Is this correct? If so, are these lines meant to be parallel? If not, for what do "g" and "h" stand? Is the slanty line meant to be a transversal, or does it stand for something else? I'd thought that "6x + 18" and "10y + 2" weren't meant to be a fraction -- but the line between them does not appear to be connected to the rest of that horizontal-ish line, so maybe they are a fraction? Either way, for what do these expressions stand? How does "3x + 9y" relate? What are the instructions? Your subject line says to "find all angles", but no angles are labelled, which makes it kinda hard to know if you've arrived at the correct values (when checking in the back of the book).

For what I'm assuming is the second exercise, you have a drawing that looks kind of like this:

Code:
nested triangles:

/\
/70\
/    \
/      \
/        \
/          \
/     ..     \
/30  .' 3'.  29\
/  .'        '.  \
/.' 1          2 '.\
*--------------------*
Unfortunately, since no other information is provided (such as whether the outer triangle is isosceles; if "1", "2", and "3" are numbers of angles, or if they're [what I'm assuming are] angle measures, like "70", "30", and "29"), it would not appear that this question in answerable. Sorry.
Sorry for being lazy. I'm referring to all to all the angles in both separate exercises. G and H refer to the 2 lines. G is parallel to H.

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#### happiness

##### Junior Member
Sorry for being lazy. I'm referring to each angle in both separate exercises. G and H refer to the 2 lines. G is parallel to H. I am currently taking Accelerated Geometry. The ones are the two seperate exercises. Posted a new picture. My bad for the inconvenience.

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#### happiness

##### Junior Member
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Lied, I thought I could change the picture. Also the 3x+9y is a corresponding angle to 6x+18
and 10y +2 is also an angle measure. They're expressions for the angle measures. The 70,30, and 29 they're the angle measures for the quadralateral angle and the 3,2, and 1 are variables. The 2, and 1 refer to the smaller triangle angle measures. It's a quadrilateral because somehow the 3 is an angle of the larger angle making the larger triangle have 4 angles that add up to 360. Sorry for being clumsy.

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#### stapel

##### Super Moderator
Staff member
Sorry for being lazy. I'm referring to all to all the angles in both separate exercises. G and H refer to the 2 lines. G is parallel to H.
So, with respect to the first exercise, the picture is actually more like the following?

Code:
lines:

6x+18 /
G -->>-------/----
10y+2 /
/
3x+9y /
H -------/--->>---
/
The lines G and H are parallel (indicated by the ">>" notation), the slanty line is a transversal, "6x + 18" and "10y + 2" do not form a fraction, and you are needing to use angle rules to create equations that you can solve for the values of "x" and "y"...?

Assuming so, where are you stuck? You used the straight-line angle sum rule to create an equation from the top two expressions. You used some other rule to create a second equation using the first and third expressions, you simplified to get a system of two equations in two unknowns, applied whatever method they've given you for solving systems of linear equations, and... then what?

Please be complete. Thank you!

#### stapel

##### Super Moderator
Staff member
The 70,30, and 29 they're the angle measures for the quadralateral angle and the 3,2, and 1 are variables.
So, for clarity's sake, let's use actual variables, rather than numbers. So the drawing should look something like the following?

Code:
nested triangles:

/\
/70\
/    \
/      \
/        \
/          \
/     ..     \
/30  .' C'.  29\
/  .'        '.  \
/.' A          B '.\
*--------------------*
The 2, and 1 refer to the smaller triangle angle measures. It's a quadrilateral...
"The smaller triangle" cannot be "a quadrilateral". Triangles have three sides; quadrilaterals have four.

...somehow the 3 is an angle of the larger angle...
I'm sorry, but I don't understand what this means...? How does your textbook define "an angle of another angle"?

...making the larger triangle have 4 angles that add up to 360.
"The larger triangle" cannot "have 4 angles that add up to 360". No triangle can have these properties.

Please reply with clarification. Thank you! ;-)

#### yma16

##### Junior Member
The left bottom angle is 10y+2

The right 4 angles from top to bottom are 10y+2, 6x+18, 10y+2, 3x+9y.
And so forth.

You can create a system of equations and solve then for x and y. Then, you can find all angles.

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#### happiness

##### Junior Member
Find each angle

Given line g is parallel to line h, find each angle. I don't know how to do thks, please show steps to solving. I do know parallel angles postulates.

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#### Dr.Peterson

##### Elite Member
Given line g is parallel to line h, find each angle. I don't know how to do thks, please show steps to solving. I do know parallel angles postulates.

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Presumably this exercise came with a picture; without seeing that, it is impossible for anyone to help!

Can you at least describe the picture, if you can't attach it, telling us where all the labeled angles are?

#### stapel

##### Super Moderator
Staff member
Given line g is parallel to line h, find each angle. I don't know how to do thks, please show steps to solving. I do know parallel angles postulates.
Okay; I've made great efforts to get you to tell us what the actual exercise is, and have created a "graphic" that people can see:

stapel said:
So, for clarity's sake, let's use actual variables, rather than numbers. So the drawing should look something like the following?

Code:
lines:

6x+18 /
G -->>-------/----
10y+2 /
/
3x+9y /
H -------/--->>---
/
The lines G and H are parallel (indicated by the ">>" notation), the slanty line is a transversal, "6x + 18" and "10y + 2" do not form a fraction, and you are needing to use angle rules to create equations that you can solve for the values of "x" and "y"...?

Assuming so, where are you stuck? You used the straight-line angle sum rule to create an equation from the top two expressions. You used some other rule to create a second equation using the first and third expressions, you simplified to get a system of two equations in two unknowns, applied whatever method they've given you for solving systems of linear equations, and... then what?
You have yet to answer the clarifying questions. I gave you "hints" for the steps to take, assuming my guesses as to your reasoning were correct, and you made no response, but then re-posted this question as a new thread (which I've now merged with the original thread).

Are you going to follow any of the "hints" you've been given? Or are you waiting for somebody to give you the complete hand-in solution? :-?

#### happiness

##### Junior Member
Sorry stapel, yma and Dr.Peterson for the confusion. Ignore the pencil writings. Given line g is parallel to line h, how do you find each angle? Please do step-by-step instructions, thanks.

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#### happiness

##### Junior Member
Sorry stapel, yma and Dr.Peterson for the confusion. Ignore the pencil writings. Given line g is parallel to line h, how do you find each angle? Please do step-by-step instructions, thanks.

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I know the parallel lines postulates as well. e.g. alternative interior, same side, corresponding.

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#### Dr.Peterson

##### Elite Member
I know the parallel lines postulates as well. e.g. alternative interior, same side, corresponding.

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You are given expressions for three angles. Which two of those angles are congruent? Write an equation expressing that fact.

How is the third angle related to the others? Write a second equation expressing that fact.

You now have a system of two equations in two unknowns, which you can solve for x and y.

#### stapel

##### Super Moderator
Staff member
Sorry stapel, yma and Dr.Peterson for the confusion. Ignore the pencil writings. Given line g is parallel to line h, how do you find each angle? Please do step-by-step instructions, thanks.
We already did this. Please study the replies you've been given in the two previous threads you started on this exercise (which have been merged now into one thread). Once again:

I created this clear and legible "drawing" for you:

Code:
lines:

6x+18 /
G -->>-------/----
10y+2 /
/
3x+9y /
H -------/--->>---
/
Then I suggested:

(i) I said to use the straight-line angle-sum rule to create an equation. To which angle expressions would this rule apply? What equation can you create from this? When you simplify this (to get the variable terms on one side of the "equals" sign and the plain number on the other), what do you get?

(ii) You can use the corresponding-angles rule to create another equation. To which angle expressions would this rule apply? What equation can you create from this? When you simplify this (to get the variable terms on one side of the "equals" sign and the plain number on the other), what do you get?

(iii) You now have a system of two equations in two unknowns. What do you get when you solve this system?

Please reply showing your work on this exercise, when you follow the step-by-step instructions. Thank you!

#### happiness

##### Junior Member
Boy oh boy...sure sounds as if you're joking...