Question

how do I solve? kind of confused.
Find the measures of each angle using the theorems. Picture shown below.

Answer 1

I know vertical angles are congruent, and that 1 and 4 and 2 and 3 will be supplementry.

Answer 2

hmm... that looks impossible...

Answer 3

1 and 3 have to be equal if these are straight lines

Answer 4

what? waaaah. ;(

Answer 5

oh, not wait, sorry, my bad

Answer 6

well, they are vertical angles so I know they are congruent.

Answer 7

I was thinking of if these lines had met at the center of the circle...

Answer 8

Does 1/3 = 2/4? Geometry theorems are not exactly fresh in my memory

Answer 9

referring to the the arcs captured by the angles

Answer 10

It would be nice if the circumference or radius of the circle was given. What theorem does the problem want you to use (it says use theorem ??)

Answer 11

4 and 2 equal 140 and 1 and 40 is what I came up with by making up a few theorems out of shear imagination and assumptions

Answer 12

That would give you a sum of 140 + 140 + 40 +40 =360 that is consistent, but how did you come up with that? Lets hear your assumptions, and reveal the imaginations.

Answer 13

well, alright, I really am not sure about anything I'll be saying from this point on, but I think it might make sense. also, (50+30)/2 = 40, so maybe that's some kind of a theorem.

let's suppose arc1/arc3 = arc2/arc4
arc2 = 360-30-50-arc4
(280-arc4)/arc4=50/30
arc4=105
arc2=175
then, for the actual angles (1=x, 2=y)
175/50= x/y
x=180-y
175/50=(180-y)/y
y =140
x=40

Disclaimer : I cannot be held responsible for a wrong answer here :-P

Answer 14

the answer was right! thank you.

Answer 15

well I'll be damned! Ok, I won't be building bridges anytime soon with that kind of reasoning, but it's still nice to know that I got some good geometry instincts ;-)

Answer 16

haha, true! thanks so much.... onto another problem that is distinctly the same. -__-

Answer 17

Your intuition was great, deserve a medal for sure @m_charron2