math destroyer test 10 #38

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demolitionlvr

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Given the following circle with center O and inscribed angel of 50 that intercepts the circle at points A and B and tangent lines from A and B that meet at external angle x. Find the measure of angle x.
View attachment Graph.png


Explanation:The measure of the central angle at O is 100, twice that of the inscribed angle of 50, since both angles meet at the same points A and B. The central angle of 50 also divides the circle into two arcs measured from side of AB, 100 and 260. The measure of the external angle x, since it is the result of the meeting of two tangents to the circle, is equal to half the difference of these intercepted arcs: x= 1/2[260-100]= 80

My confusion:
The bolded part..where is 260 from?

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It's the measure of the larger arc, basically the circle is split into two different arcs that can both be called "AB". So the smaller arc is 100 degrees and 360-100 = 260 for the larger arc.

On a sidenote I don't recall every learning this arc stuff ever haha, all the other stuff I knew at one point and forgot don't recall this stuff at all...
 
What ralph said is correct,

I remember seeing 3 or more of these circle problems on math destroyer.

1 was almost exactly like this; however, they didn't use tangent lines. On a side rant, those lines don't look tangent to me!
 
sorry to bring back an old thread but I'm also having trouble with this problem. How do you know to subtract the two arcs and divide by 2?

can anyone clarify this please?
 
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sorry to bring back an old thread but I'm also having trouble with this problem. How do you know to subtract the two arcs and divide by 2?

can anyone clarify this please?

It's simply a rule in geometry with these types of problems: the measure of the angle = (big arc - small arc)/2
 
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