e circle, will not divide the circle without having the
last division either too long or too short, in which case the circle may
be divided as follows: The compasses set to its radius, or half its
diameter, will divide the circle into 6 equal divisions, and each of
these divisions will contain 60 degrees of angle, because 360 (the
number of degrees in the whole circle) /6 (the number of divisions) =
60, the number of degrees in each division. We may, therefore, subdivide
as many of the divisions as are necessary for the two lines whose
degrees of angle are to be found. Thus, in Figure 59, are two lines, C,
D, and it is required to find their angle one to the other. The circle
is divided into six divisions, marked respectively from 1 to 6, the
division being made from the intersection of line C with the circle. As
both lines fall within less than a division, we subdivide that division
as by arcs _a_, _b_, which divide it into three equal divisions, of
which the lines occupy one division. Hence, it is clear that they are at
an angle of 20 degrees, because twenty is one-third of sixty. When the
number of degrees of angle between two lines is less than 90, the lines
are said to form an acute angle one to the other, but when they are at
more than 90 degrees of angle they are said to form an obtuse angle.
Thus, in Figure 60, A and C are at an acute angle, while B and C are at
an obtuse angle. F and G form an acute angle one to the other, as also
do G and B, while H and A are at an obtuse angle. Between I and J there
are 90 degrees of angle; hence they form neither an acute nor an obtuse
angle, but what is termed a right-angle, or an angle of 90 degrees. E
and B are at an obtuse angle. Thus it will be perceived that it is the
amount of inclination of one line to another that determines its angle,
irrespective of the positions of the lines, with respect to the circle.

[Illustration: Fig. 60.]

TRIANGLES.

A right-angled triangle is one in which two of the sides are at a right
angle one to the other. Figure 61 represents a right-angled triangle, A
and B forming a right angle. The side opposite, as C, is called the
hypothenuse. The other sides, A and B, are called respectively the base
and the perpendicular.

[Illustration: Fig. 61.]

[Illustration: Fig. 62.]

[Illustration: Fig. 63.]

[Illustration: Fig. 64.]

An acute-angled triangle has all its angles acute, as in Figure 63.

An obtuse-angled triangle has one obt