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In the figure given alongside, what do we mean by ∠P?

Here, ∠P can be considered any of the three angles ∠APB, ∠BPC or ∠APC. So, A
it is necessary to use three letters to specify an angle clearly.
P B

Knowledge Desk C

Pierre Herigone (1580-1643) used < and ∠ symbol in his book Cursus mathematicus
for angle. This work was published in 1634.

Interior and Exterior of an Angle

Let us consider an angle, say ∠ABC. First, we shade the portion of the paper above ray BA . Then,

we shade the portion of the paper below ray BC .

C
C C

B
B B

A
A A

Observe the portion bordering rays BA and BC , which has double shading. This shows the interior
of angle ABC. (Note that the interior is not a restricted area; it extends indefinitely since the two
sides extend indefinitely).

Thus, an angle divides the plane into three parts:

• Interior of an angle: The region between two arms of an angle is called A
interior of that angle. In the given figure, points P, Q and R lie in the E N R
interior of ∠ABC. P
Q
• Exterior of an angle: The region outside both arms of an angle is called B
exterior of an angle. In the given figure, points D, E and F lie in the M D C F

exterior of ∠ABC.
• Angle itself (Boundary of an angle): Points that lie on the arms of the angle (e.g., points A, B,
C, M, and N).

Example 7: In the given figure, name the point(s):
F
(a) in the interior of ∠DOE
C E
(b) in the exterior of ∠EOF A
B
(c) on ∠EOF O
D
Solution: From the given figure, we observe that:

(a) Point A lies in the interior of ∠DOE.
(b) Points C, A and D lie in the exterior of ∠EOF.

(c) Points E, B, O and F lie on ∠EOF.

37 Lines and Angles