Ex. 7.—Upon a straight line to draw an angle equal to a given angle, [Fig. 110]. Let A be the given angle and F G the line. With any radius from the points A and F, describe arcs D E, I H, cutting the sides of the angle A and the line F G.
Set off the arc I H, equal to D E and draw F H. The angle F is equal to A as required.
Fig. 111.
Ex. 8.—To bisect an angle, [Fig. 111]. Let A C B be the angle; on the center C cut the sides at A B. On A and B as centers describe arcs cutting at D dividing the angle into two equal parts.
Fig. 112.
Ex. 9.—To find the center of a circle or of an arc of a circle. [Fig. 112]. Draw the chord A B, bisect it by the perpendicular C D, bounded both ways by the circle; and bisect C D for the center G.
Fig. 113.