Measuring Angles Without a ProtractorDate: 01/26/99 at 22:41:37 From: Maggie Jabakchourian Subject: Measuring angles without using a PROTRACTOR. Hi, My little sister is in the 6th grade, and her teacher gave her a question on measuring angles without using a protractor. We tried to figure it out by adding all the angles and subtracting the total from 180 degrees. I was wondering if you might tell me another method of doing this by helping with this sample problem. A trapezoid is drawn with four sides, labeled 1, 2, and 3. On the left top side of the trapezoid there is 60 degree angle shown. The problem states to find out the angles of 1, 2, and 3. How would we go about finding the answer? Any help would be greatly appreciated. Thank you. Date: 01/27/99 at 12:29:34 From: Doctor Peterson Subject: Re: Measuring angles without using a PROTRACTOR. Hi, Maggie. There's a little missing in your description, since without extra information you can't figure out all the angles. I'm going to assume you have an isosceles trapezoid like this, where you know that sides B and D are the same length: A +---------------------------------------+ \60 (3)/ \ / \ / D \ / B \ / \ / \(1) (2)/ +-----------------------+ C Your idea of subtracting from 180 would work in a triangle, but you need slightly different tricks here. You know two important things: in a trapezoid, sides A and C are parallel; in an isoceles trapezoid, not only are sides B and D equal, but angles 1 and 2 are equal. For parallel lines, \ -------------+--------------- \a \ b\c -----------------+----------- \ angles a and b are equal, and angles b and c are supplementary (they add up to 180). From this you can get (1); from that you can get (2); and from that (or directly) you can get (3). If the trapezoid is not isosceles, you can't tell what (2) and (3) are, because they could be anything: A +-------------------------------+ \60 (3)| \ | \ | D \ | B \ | \ | \(1) (2)| +-----------------------+ C - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/ |
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