## brookieismyname 3 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. brookieismyname

2. integralsabiti

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3. brookieismyname

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4. imagreencat

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

5. integralsabiti

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6. brookieismyname

What does that say?

7. brookieismyname

I need to know how to find the measure of abc

8. imagreencat

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. brookieismyname

Thats not one of the options though

10. integralsabiti

@eigenschmeigen take a look at this pls.

11. eigenschmeigen

yeah i got 50 ill show:

12. smr_kml

13. smr_kml

14. estudier

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

15. eigenschmeigen

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16. integralsabiti

@eigenschmeigen my man! love ur answers :D

17. smr_kml

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18. eigenschmeigen

|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. brookieismyname

The only problem is fifty's not an option

20. eigenschmeigen

aw thanks @integralsabiti :D means a lot to me

21. integralsabiti

oh yeaaa :D that is the best part!

22. eigenschmeigen

hmm 50 isnt an answer is it

23. brookieismyname

No

24. integralsabiti

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

25. eigenschmeigen

haha

26. smr_kml

:D

27. eigenschmeigen

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

28. eigenschmeigen

i cant see any errors :/

29. eigenschmeigen

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

30. integralsabiti

Abselutely agree.

31. brookieismyname

The answer was 65 degrees, @eigenschmeigen @integralsabiti

32. eigenschmeigen

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. eigenschmeigen

34. brookieismyname

A test

35. eigenschmeigen

and you're sure its 130?

36. brookieismyname

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