<p>I'm sorry, but could someone explain this question to me: </p>
<p>"Find the arc measure of the arc cut by one side of a circumscribed regular hexagon." </p>
<p>F. 30 degrees
G. 60 ''
H. 120 ''
J. 180 ''
K. 240 ''</p>
<p>I don't even fully understand the question - does circumscribed mean the hexagon is inside the circle or is the circle inside the hexagon? I ask this question because I googled circumscribed hexagon and got both cases. </p>
<p>If the hexagon is inside the circle, then I think the answer is 60 degrees because there must be an arc cut for every side of the hexagon (6) and so its 60 degrees each. I still hesitate because the explanation given in the book (This is the Barrons 36 book) is as follows: </p>
<p>"One angle of a regular hexagon is 120 degrees and it cuts the corresponding arc to result in a measure of 240 degrees. That leaves 120 degrees to be divided by two chords that are equivalent in length making each arc measure 60 degrees." </p>
<p>I have absolutely no idea what that means. </p>
<p>The second question I have, has an illustration (question 45 of the math practice test in the same book - page 162) that I can't put up but if anyone has the book, I'd really appreciate some help.</p>
<p>okay
since the angle is 120, there’s a geometry theorem that says that the arc corresponding to that angle is twice the measure.</p>
<p>so the arc is 240
360 degress in a circle, so 360-240=120
you have 120 left
and you divide that by 2
because the vertex of the angle splits it evenly</p>
<p>Thanks megustamath, but I don’t really understand that. </p>
<p>Wouldn’t the angle be the same as the arc corresponding to it? Like a quarter of a circle is 90 degrees and its arc would also be 90 degrees right? </p>
<p>Also is the circle inside the hexagon or the other way around? I’m really sorry guys, I haven’t done geometry in 4 years and I’ve forgotten it all. Plus I’m not very good at math…</p>
<p>Carbon,
The reason it doesn’t correspond is because the 120 degree angle isn’t coming from the center of the circle/hexagon figure. It is coming from an end of it, which requires you to use the “the arc corresponding to that angle is twice the measure” rule that megustamath mentioned earlier. Therefore, the corresponding arc would be 240.</p>
<p>Seeing as how this was posted two years ago and might not be helpful to you now, I hope this might be helpful to someone else dealing with the same problem.</p>