Question

If the measure of arc AC is 140°, what is the measure of angle ABC?

Answer 1

ITs 40 degrees

Answer 2

angle ABC= 360 -140 -ACB - CAB

Answer 3

@arabpride, without one more piece of data, how do you determine it is 40, and by proxy that the 2 remaining angles are 90? (which it is drawn semi to scale they cannot be)

without knowing those are 90, how do we claim that they are?

Answer 4

i thought it was 360 - 140

Answer 5

They are tangents to the circle.

Answer 6

if B was closer or further from the circle than it is, that would not be true. there is nothing that says how far away B is so isn't that a huge assumption? where's the geometry/trig proof?

Answer 7

tangent to a circle is always at right angle to the radius of the circle at the point of contact.

Answer 8

ok so i got 360-140 = 220 ...

Answer 9

it cant be 220 because there are still two side angle unaccounted for

Answer 10

220 represent the 3 remaining angles. 2 of them will be identical but there are an infinite number of solutions until we know the distance that B is from the circle

Answer 11

sum of four angles of a quadrilateral =360
140+90+<ABC+90=360

Answer 12

how (mathematically) can you claim that the 2 side angles are 90?

Im not trying to be a pain, just seeking to understand

Answer 13

shall i do 220 - 180?

Answer 14

they could be 89 degrees for all you know based on the info given...

Answer 15

my first answer is correct until more data is given

Answer 16

360 - 140 - the two unknown angles = andgle ABC

Answer 17

I see your drawing where you "claim" that the sides are 90.
I have yet to hear or see logical reason to accept it

Answer 18

what if they are 89 degrees? how do you prove it?

Answer 19

nothing states that they are right angles...

Answer 20

there are no right angles here

Answer 21

again, just seeking to understand, not just blindly accept