brookieismyname
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°
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integralsabiti
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brookieismyname
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imagreencat
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Arc AC is the part of the circle connecting A and C. It lies on the circumference of the circle.
integralsabiti
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brookieismyname
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What does that say?
brookieismyname
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I need to know how to find the measure of abc
imagreencat
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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.
brookieismyname
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Thats not one of the options though
integralsabiti
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@eigenschmeigen take a look at this pls.
eigenschmeigen
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yeah i got 50
ill show:
smr_kml
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There is no right answer
smr_kml
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the answer is 50
estudier
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I aslo get 50 (draw line from centre to B, Pythagorus)
eigenschmeigen
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integralsabiti
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@eigenschmeigen my man! love ur answers :D
smr_kml
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eigenschmeigen
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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\[\alpha = 360 - 90 -90 -130 = 50\]
brookieismyname
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The only problem is fifty's not an option
eigenschmeigen
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aw thanks @integralsabiti :D means a lot to me
integralsabiti
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oh yeaaa :D that is the best part!
eigenschmeigen
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hmm 50 isnt an answer is it
brookieismyname
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No
integralsabiti
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if @eigenschmeigen says that the answer is 50 then u should make a new option :D option E.
eigenschmeigen
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haha
smr_kml
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:D
eigenschmeigen
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i'll check through the problem see if we missed something
eigenschmeigen
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i cant see any errors :/
eigenschmeigen
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i checked it using some geometry software, its 50 for sure
integralsabiti
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Abselutely agree.
brookieismyname
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The answer was 65 degrees, @eigenschmeigen @integralsabiti
eigenschmeigen
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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?
eigenschmeigen
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brookieismyname
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A test
eigenschmeigen
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and you're sure its 130?
brookieismyname
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I got it right, I guessed the right answer. It was 65