Circles Articles - Wyzant Tutor Blogshttps://www.wyzant.com/resources/blogs/circlesThis is an aggregate of all of the Circles articles in Wyzant.com's Tutors' Blogs. Wyzant.com is your source for tutors and students.Tue, 21 Jan 2020 08:24:31 -0600https://www.wyzant.com/images/logos/wyzant-logo.pngCircles Articles - Wyzant Tutor Blogshttps://www.wyzant.com/resources/blogs/circleshttps://www.wyzant.com/resources/blogs/circles546595https://www.wyzant.com/resources/blogs/546595/constructing_angles_without_a_protractorJon A.https://www.wyzant.com/resources/users/view/80232370Constructing angles without a protractor<div>A student needed to draw a circle with a 2" diameter, then draw the following angles: 100°, 120º, and 140º. She had her compass but didn't have her protractor.</div>
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<div>First she drew the circle, then she drew 2 perpendicular diameters. Since a circle encompasses 360º, each quadrant comprising 90º. We drew the 120º angle first using an entire 90º quadrant plus 1/3 of the adjacent quadrant, erasing the unneeded line, which leaves 60º in that second quadrant.</div>
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<div>Then we found the circumference of the circle (C=πD, or 3.14x2"=6.28"). Next we found 1/4 of the circumference (6.28"/4=1.57"). We wanted to be able find the arc length in 10º increments, so we divided the arc of one quadrant by 9 (1.57"/9=0.174"). We converted this into 1/16ths of an inch by multiplying by 16 (0.174"x16=2.79 sixteenths of an inch).</div>
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<div>Getting back to our angles, we measured the 100º angle next by taking our remaining 60º and adding 40º of arc length to it (4x2.79=11.16 sixteenths). Note: It may be helpful to mark sixteenths of an inch along the arc and reposition the ruler after each. The final 140º angle arises naturally.</div>
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<div>Hope this helps if you (or a student) needs to construct angles without a protractor. :)</div>Tue, 09 May 2017 23:34:23 -05002017-05-09T23:34:23-05:00