Question

http://prntscr.com/2rb1zi

Answer 1

http://www.regentsprep.org/Regents/math/geometry/GP5/LExtAng.htm

Answer 2

so which one do you think?

Answer 3

my answer is 8

Answer 4

do you know what the external theorem is?

Answer 5

is <8 really wiser than < 13?

Answer 6

no and 8 is not wiser then 13

Answer 7

erk, I meant WIDER

well, if it's not wider.... that doesn't sound very feasible

Answer 8

oh idk lol

Answer 9

http://www.regentsprep.org/Regents/math/geometry/GP5/LExtAng.htm <--- external angle theorem

Answer 10

based on the theorem then we can say that \(\bf \measuredangle {\color{red}{ 13}} = \measuredangle 10 +\measuredangle 2\qquad and \qquad \measuredangle {\color{red}{ 13}} = \measuredangle 1 + \measuredangle 8\)

so as you can see, those angles cannot be greater or wider than 13
so that'd leave you with a choice

Answer 11

hmmm

Answer 12

I think I say that a bit off... lemme rewrite that .... since \(\bf 13 \ne 10\)

Answer 13

\(\bf \measuredangle {\color{red}{ 13}} = \measuredangle 10 +\measuredangle 2\qquad and \qquad \measuredangle {\color{red}{ 13}} = \measuredangle (1 + 2) \measuredangle (8+7)\)

so. any of those angles are ruled out due to the external angle theorem

Answer 14

so the answer would be 10?

Answer 15

did you understand the theorem? maybe you'd just need a quick walkthrough

Answer 16

yeah i don't really know all this stuff

Answer 17

oh ok

Answer 18

so those 2 other angles, since both of them will SUM UP to the external, then both of them have to be SMALLER than the external and thus
cannot be bigger or wider than the external on any given figure

Answer 19

so notice on those 2 triangles there, the other 2 angles on the opposite end

Answer 20

hmmm.... come to notice, my original posting was ... correct... anyhow lemme correct that

that picture shows that \(\bf \measuredangle {\color{red}{ 13}} = \measuredangle 10 +\measuredangle 2\qquad and \qquad \measuredangle {\color{red}{ 13}} = \measuredangle 1 + \measuredangle 8\)

Answer 21

so, therefore, 10 or 12 or 1 or 8, are smaller or narrower than 13

Answer 22

oh its 9

Answer 23

oh its 9 \(\Large \checkmark\)

Answer 24

Thanks :)

Answer 25

notice, 9 is really wide

Answer 26

yes

Answer 27

\(\bf \bf \measuredangle {\color{red}{ 13}} = \measuredangle 10 +\measuredangle 2\qquad and \qquad \measuredangle {\color{red}{ 13}} = \measuredangle (1 +2) \measuredangle 8\) anyhow....