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°

- anonymous

- chestercat

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- anonymous

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- anonymous

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- anonymous

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## More answers

- anonymous

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

- anonymous

|dw:1335033299166:dw|

- anonymous

What does that say?

- anonymous

I need to know how to find the measure of abc

- 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.

- anonymous

Thats not one of the options though

- anonymous

@eigenschmeigen take a look at this pls.

- anonymous

yeah i got 50
ill show:

- anonymous

There is no right answer

- anonymous

the answer is 50

- anonymous

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

- anonymous

|dw:1335033823663:dw|

- anonymous

@eigenschmeigen my man! love ur answers :D

- anonymous

|dw:1335033908901:dw|

- 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\[\alpha = 360 - 90 -90 -130 = 50\]

- anonymous

The only problem is fifty's not an option

- anonymous

aw thanks @integralsabiti :D means a lot to me

- anonymous

oh yeaaa :D that is the best part!

- anonymous

hmm 50 isnt an answer is it

- anonymous

No

- anonymous

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

- anonymous

haha

- anonymous

:D

- anonymous

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

- anonymous

i cant see any errors :/

- anonymous

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

- anonymous

Abselutely agree.

- anonymous

The answer was 65 degrees, @eigenschmeigen @integralsabiti

- 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?

- anonymous

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- anonymous

A test

- anonymous

and you're sure its 130?

- anonymous

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

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