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# how do i measure angles without a protractor

Question:I need to know how to do this, I have lost my protractor. I don't know what trigonometry is so if you suggest it can you explain it to me please? Also can you explain it simply please? thankyou it is much appreciated:)

Answers:Two ways you can do it. 1) You can approximate it. Draw a 90 degree angle, cut it in 3 equal slices, and the second slice closest to the 90 degree would be approximately 60 degrees. 2) Use a coordinate plane. Draw a line in which the tangent line of the origin is 60 degrees. Y = mx + b, b = 0 since it's a point in the origin. m is going to be the slope. tan(slope) = 60 degrees, so, the arctan(60) = slope. arctan(60) = 3 divided by the square root of 3. Therefore, the line must be: y = 3/(square root of 3) * x Just use the coordinate plane to plot the points of that equation and there you have a line with a 60 degree angle. :P The second one would of course get you a much more accurate 60 degree angle, especially if you graph it on graphing paper. :] I <3 graphing paper.

Question:This is part of a bonus question for a quiz I'm taking in Geometry. I can't use a protractor at all but I can use a ruler and a compass. Also, I highly doubt we can fold the quiz paper and it's not square.

Answers:you could draw one with a protractor and then use a compass and straightedge to copy the angle exactly. If you don't have a protractor, then i'm sorry. To draw the construction, draw a line, then use the compass to mark the distance from the vertex and copy this distance onto the line you drew. Then, with that same distance, draw an arc about 105 degrees. Then from the point where you know by measuring the distance, draw an arc that will intersect with the just drawn one. From this point, draw a line through it and the vertex and there you go. Look on the internet for a finer explanation

Question:I know that you have to put the center of the protractor onto the middle of the circle right above the 90 degrees, but if they give you a bunch of numbers to make a circle graph with how do you use the protractor? For example, it gives you 34.6, 29.5, 15.2, 12.7, and 8 to put onto the graph. First I know you have to find angle measurements. But how do you place it into the graph?

Answers:You put the bottom flat edge on the line that is 0. draw a line. then mark the degree that you want. then draw a straight line from the center to the mark that you just made.good luck

Question:it should be done only by the help of pencil, compass(simple) and scale, no paper fold, no mumbo-jumbo!

Answers:Hi, You may be aware that the smallest *integer* angle that can be constructed *perfectly* is 3 degrees. Both 72 degrees and 60 degrees can be constructed perfectly. 72 degrees divided by 4 is 18 degrees and 60 divided by 4 is 15 degrees. When the two are constructed adjacent to each other, you get 18-15 degress, which results in a three degree angle. The angle of 1 degree cannot be constructed perfectly under Euclidean rules (compasses and straight edge only) because it implies a trisection (of 3 degrees), and trisection has been proved impossible. The question remains as to what variance would be acceptable in your necessarily approximate construction of the 1 degree angle?