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Or by another method. A radius, if made a cord of the semicircle, will allow three cords, each of which will contain 60 degrees; halve these arcs, and you have arcs of 30 degrees; halve the arcs of 30 degrees, and you have 15 degrees; cut these into three equal parts, and you have 5 degrees; then divide the arcs of five degrees into five parts, and you have the 180 degrees of the semicircle.
Whether the circle be large or small, it is divided into the same number of degrees; for if the radii of a small circle be lengthened out, and a larger circle drawn from the same centre, the radii will form the same part of the large as of the small circle, and the angle between any two radii will be unchanged.
9. Make an angle of 30 degrees on the graduated semicircle. (fig. 4.)
A radius drawn from the centre to the number 30 on the graduated semicircle, will form an angle of 30 degrees with the diameter of the semicircle. And so for any other number of degrees. It will be seen that any number of degrees less than 90 will make an acute angle, and more than 90 degrees will form an obtuse angle thus, in fig. 4, 30 degrees form an acute angle, and the remaining 150 degrees of the half circle form an obtuse angle.
Angles, therefore, are measured by their openings. Place the point of angle on the centre of the semi-circle, or the centre of the semicircle on the point of the angle, and then by seeing how many degrees the opening of the angle measures on the graduated edge of the semicircle, you will find the size of the angle. If the sides of the angle do not extend to the circumference, you may extend them till they do. If they extend beyond the circumference, measure the angle where the graduated circle cuts the sides.
