Question

Which inequality is false?

Click Here for a long description of the image above.
A. angle14 > angle11
B. angle10 > angle5
C. angle2 > angle11
D. angle 15 > angle4

Answer 1

We're going to need the drawing for this one.

Answer 2

Don't you just hate these 'complex' geometric systems where you have to look at each component individually?
In fact, in this question, you need to look at the right components :D

Answer 3

i just hate geometry in general, i dont understand any of it ): hah

Answer 4

Well that's a pity :)

The best I can do here is remind you of the External Angle Theorem.
It states that the angle measure of an external angle of a triangle is equal to the sum of the measures of its two remote angles...

Answer 5

To illustrate...

Answer 6

Here, angle A is the external angle, and its measure is equal to the sum of the measures of angles M and N.

The theorem simply states that for any such configuration of triangle, A = M + N

Answer 7

A = M + N, of course, implying both
A > M
and
A > N

Answer 8

Let's take choice B, for instance...

Answer 9

Do you see this part in your drawing?

Answer 10

yep!

Answer 11

Well, which of these angles is the external angle?

Answer 12

angle 10 ?

Answer 13

Yes :)
so by the theorem,
angle 10 = angle 5 + angle 4
correct?

Answer 14

i believe so!

Answer 15

So, since angle 10 is equal to the sum of angles 4 and 5, you can bet that it'd be bigger than both of these angles individually

So...
angle 10 > angle 4
and
angle 10 > angle 5

yes?

Answer 16

yess!

Answer 17

So B is true... and therefore not the correct answer :3

Answer 18

Do you want to check another choice?

Answer 19

i think i got this now! (: thanks so much!!

Answer 20

Okay, which is your answer?

Answer 21

i think its A !?

Answer 22

Let's check that...

Answer 23

What is the external angle here?

Answer 24

14.

Answer 25

That's right :)
What are the remote angles of angle 14?

Answer 26

it would be 4, 5 and 11, no ?

Answer 27

Remote angles = the angles in the triangle that are not beside the external angle.

Answer 28

No, there are only two remote angles :P

Answer 29

ohp so minus the 4 then.

Answer 30

Right :)
So (14) [I'll just put the angle in parentheses, I hope you don't mind]
is the external angle while
(5) and (11) are its remote angles.

By the EAT (External Angle Theorem)
What do we get?

Answer 31

Remember, EAT states that the external angle is equal to THE SUM of the remote angles...

Answer 32

wait, i guess i dont know then ..

Answer 33

baah. im so lost. dangit

Answer 34

Hopefully, I just have to say this once more :)
Please understand the concept :)

the external angle is (14)
its remote angles are (5) and (11)
therefore, by EAT

(14) = (5) + (11)

Answer 35

... fine, it looks bad to me...
angle(14) = angle(5) + angle(11)

Answer 36

oh then yeah, i had that. my bad, for some reason i thought you threw something else at me, cause of the EAT ha

Answer 37

Okay, once again, angle(14) is equal to THE SUM of angle(5) and angle(11)
So, you can bet that it'd be bigger than both of these angles individually... namely, that

angle(14) > angle(5)

AND

angle(14) > angle(11)

So angle(14) > angle(11) is true... so A is not your answer, unfortunately :P

Answer 38

well its either A or D then, so since its not a or b that makes it D no ?

Answer 39

to tired for this nonsense. -_-

Answer 40

Most unfortunately, this 'nonsense' would never get tired of tormenting you :D
Now let's try D again... but this is the third test, so I expect you take the lead in checking it, okay? :)

Answer 41

Okay, what's the external angle this time?

Answer 42

15

Answer 43

Okay.. and what are its remote angles?

Answer 44

so the remote angles would be 4 and 11

Answer 45

correct, so by EAT, what can we conclude?

Answer 46

so 15 = 5 + 11 ??

Answer 47

Yes. Please put angle... it really makes me feel uncomfortable, seeing
15 = 5 + 11
>:D

Answer 48

So anyway, since (15) is the sum of (5) and (11)
Then 15 is bigger than...?

Answer 49

angle15 > angle5
and
angle15> angle 11

???

Answer 50

Yes, making choice D... (true/false)?

Answer 51

true /

Answer 52

Which means it's not your correct answer....

LOL It musn't be your day....

I basically gave you three tries to find the correct answer out of four choices and you gave me all three wrong answers XD

Answer 53

We now know A, B, and D are wrong... so.. :3

Answer 54

C . thanks.

Answer 55

No more guessing next time, okay? Promise? :)