Question

Using the exterior angle theorem determine which angle measures is not greater than angle four. My choices are angle 12, angle 15, angle 6 or angle 10.

Answer 1

The exterior angle theorem is Proposition 1.16 in Euclid's Elements, which states that the measure of an exterior angle of a triangle is greater than either of the measures of the remote interior angles. This is a fundamental result in absolute geometry because its proof does not depend upon the parallel postulate.

is there like a picture to this problem??

Answer 2

trying to paste it now

Answer 3

:))

Answer 4

can you see attachments

Answer 5

can you look at the attachment and help me figure out the problem for exterior angles

Answer 6

hmm I dont see the answer that is right...

Answer 7

what answer do u think it should be. I was also confused

Answer 8

6 or 10...

Answer 9

Sorry I couldnt quite help.. :(((

Answer 10

ok thanks

Answer 11

Are you sure you copied your question correctly?

Answer 12

yes

Answer 13

You wrote in the problem:
"Using the exterior angle theorem determine which angle measures is not greater than angle four."

How can you have "angle measures" and then "is not greater"
"is" goes with a singular subject.
Also, are you sure the word "not" belongs there?

Answer 14

I realize the "s" is incorrect but that was the problem and the word not is part of the question. It seems like it is incorrect becs. I can't come up with an answer from the 4 choices. Can you?

Answer 15

The exterior angle theorem states that in a triangle, the measure of an exterior angle is greater than either of the measures of the two remote interior angles.

Answer 16

Angle 4 in your figure is an interior angle of a triangle.

Answer 17

so it is a remote angle

Answer 18

If you can find an exterior angle of that triangle for which angle 4 is a remote interior angle, then you can state that that exterior angle has a greater measure than the measure of angle 4. That is what the exterior angle theorem allows you to do.

Answer 19

I understand the ext. angle theorem but couldn't relate it to this problem. I thought I was missing something. Probably the question is written incorrectly but not on my part.

Answer 20

The problem is that according to the wording of your problem, you are not looking for an exterior angle whose measure is greater than angle 4. You are looking for an exterior angle whose measure is not greater than angle 4. That can't be done.

Answer 21

agree, I need to have my teacher reanalyze this question

Answer 22

Just like you copied the figure and showed it as a file, can you do the same with the wording of the problem?

Answer 23

I couldn't figure out how to copy the diagram, my brother did it for me and he has left. however, I have rechecked the wording and it is exact.

Answer 24

Ok, thanks.

Answer 25

thanks for your help. I will follow up with teacher tomorrow.

Answer 26

Ok. Here's an idea.
Looking at angle 4 as an interior angle of one of the triangles in the figure, can you name any remote exterior angles to angle 4?

Answer 27

If looking at the small triangle with angle 4 I think 15, 12, 6 and 10 are all exterior to 4

Answer 28

Actually, close, but one of those is not an exterior angle of the triangle.
Angles 10, 12, and 15 are remote exterior angles to angle 4.
Angle 6 is not a remoter exterior angle because it is not an exterior angle of the triangle at all.
According to the exterior angle theorem, we know that angles 10, 12, and 15 must have a larger measure than angle 4.
The answer is angle 6.

Answer 29

I don't see why 6 isn't an exterior angle to angle 4 if angle 12 is an exterior, why not 6?

Answer 30

The problem with your problem is the wording is not good.
According to the exterior angle theorem, we know that angles 10, 12, and 15 have a greater measure than angle 4 because they are remote exterior angles to interior angle 4.
Since angle 6 is not a remote exterior angle of this triangle, we don't know anything about its measure.

Your problem should be worded like this:
"Using the exterior angle theorem determine which angle measures is not necessarily greater than angle four. My choices are angle 12, angle 15, angle 6 or angle 10."

Answer 31

Ok. I'll show you why angle 6 is not an exterior angle.

Answer 32

Just to be sure, the triangle we are using with angle 4 has angles 4, 11, and 5, right?

Answer 33

yep

Answer 34

Angles 10, 12, 14, 15 are the only exterior angles of our triangle that are shown.

Answer 35

All other angles shown are not exterior angles of our triangle.

Answer 36

ok now I can visualize the angles

Answer 37

thanks for sticking with the weirdly worded problem

Answer 38

Remember, an exterior angle has to be formed with the extensions of the sides of a polygon. Also, it must use one side of the polygon.

Answer 39

Triangle with 3 interior angles labeled 1, 2, 3.

Answer 40

Now let's look at the exterior angles.
There are two at each vertex.

Answer 41

Angles A, B, C, D, E, F are exterior angles.
There are no other exterior angles.
The angle at each vertex that is vertical with each interior angle is NOT an exterior angle.

Answer 42

I submitted my answer angle 6 and that was correct. I thought I knew exterior angles but you have explained it better to me.

Answer 43

In your problem, angle 15 and the large angle marked below angle 15 are two exterior angles of our triangle. Angle 6 is not.