## anonymous 4 years ago The circle shown below has AB and BC as its tangents. If the measure of arc AC is 130°, what is the measure of angle ABC? 80° 65° 70° 75°

1. anonymous

2. anonymous

|dw:1335032976626:dw|

3. anonymous

|dw:1335033326418:dw|

4. anonymous

Arc AC is the part of the circle connecting A and C. It lies on the circumference of the circle.

5. anonymous

|dw:1335033299166:dw|

6. anonymous

What does that say?

7. anonymous

I need to know how to find the measure of abc

8. anonymous

The angle is actually equal to the (far arch-near arc)/2. The far arc is the one farther from the angle unknown. Since near arc = 130, far arc = 230. Therefore, the unknown angle is (230-130)(1/2) = (100/2) = 50 deg.

9. anonymous

Thats not one of the options though

10. anonymous

@eigenschmeigen take a look at this pls.

11. anonymous

yeah i got 50 ill show:

12. anonymous

13. anonymous

14. anonymous

I aslo get 50 (draw line from centre to B, Pythagorus)

15. anonymous

|dw:1335033823663:dw|

16. anonymous

@eigenschmeigen my man! love ur answers :D

17. anonymous

|dw:1335033908901:dw|

18. anonymous

|dw:1335033879923:dw| break it into two triangles, and we know triangles have interior angles that add up to 180 so that quadrilateral has 360 as the sum of its interior angles so $130 + 90 + 90 +\alpha = 360$ so$\alpha = 360 - 90 -90 -130 = 50$

19. anonymous

The only problem is fifty's not an option

20. anonymous

aw thanks @integralsabiti :D means a lot to me

21. anonymous

oh yeaaa :D that is the best part!

22. anonymous

hmm 50 isnt an answer is it

23. anonymous

No

24. anonymous

if @eigenschmeigen says that the answer is 50 then u should make a new option :D option E.

25. anonymous

haha

26. anonymous

:D

27. anonymous

i'll check through the problem see if we missed something

28. anonymous

i cant see any errors :/

29. anonymous

i checked it using some geometry software, its 50 for sure

30. anonymous

Abselutely agree.

31. anonymous

The answer was 65 degrees, @eigenschmeigen @integralsabiti

32. anonymous

im sorry, but either the answers are wrong or have written the question wrong i say this in the nicest possible way of course :) where was this question from?

33. anonymous

34. anonymous

A test

35. anonymous

and you're sure its 130?

36. anonymous

I got it right, I guessed the right answer. It was 65