Mrs. B. Well then, let the line A B ([plate 2. fig. 1.]) represent the floor of the room, and the line C D that in which you throw a ball against it; the line C D, you will observe, forms two angles with the line A B, and those two angles are equal.
Emily. How can the angles be equal, while the lines which compose them are of unequal length?
Mrs. B. An angle is not measured by the length of the lines, but by their opening, or the space between them.
Emily. Yet the longer the lines are, the greater is the opening between them.
Mrs. B. Take a pair of compasses and draw a circle over these spaces, making the angular point the centre.
Emily. To what extent must I open the compasses?
Mrs. B. You may draw the circle what size you please, provided that it cuts the lines of the angles we are to measure. All circles, of whatever dimensions, are supposed to be divided into 360 equal parts, called degrees; the opening of an angle, being therefore a portion of a circle, must contain a certain number of degrees: the larger the angle the greater is the number of degrees, and two angles are said to be equal, when they contain an equal number of degrees.
Emily. Now I understand it. As the dimension of an angle depends upon the number of degrees contained between its lines, it is the opening, and not the length of its lines, which determines the size of the angle.
Mrs. B. Very well: now that you have a clear idea of the dimensions of angles, can you tell me how many degrees are contained in the two angles formed by one line falling perpendicularly on another, as in the figure I have just drawn?