Page 49 - Ganit Kaushal

Some Special Kinds of Angles

Based on their degree measurement, we can redefine a few special types of angles:
Acute angle - An angle whose measure lies between 0° and 90° is called an acute angle.
Right angle - An angle whose measure is 90° is called a right angle. It is a quarter of the full circle (turn).

Obtuse angle - An angle whose measure lies between 90° and 180° is called an obtuse angle.
Straight angle - An angle whose measure is 180° is called a straight angle. It is half of the full circle (turn).
Reflex angle - An angle whose measure lies between 180° and 360° is called a reflex angle.

Complete angle - An angle whose measure is 360° is called a complete angle. It is one full circle (turn), or
one revolution.

How to Measure a Reflex Angle

To measure the reflex ∠x in the given figure, first we have to measure ∠y with the help of a protractor.

Since ∠x and ∠y together make a full circle, B C
⇒ ∠x + ∠y = 360°
y
⇒ ∠x = 360° – ∠y; A

Substituting the value of ∠y in this equation will give us the value of reflex ∠x. x
Suppose that ∠y = 110°, then ∠x = 360° – 110° = 250°

Solved Examples

Ex 1. Match the following:

(i) Straight angle (a) Less than one-fourth of a revolution
(ii) Right angle (b) More than half of a revolution
(iii) Acute angle (c) Half of a revolution
(iv) Obtuse angle (d) One-fourth of a revolution
(v) Reflex angle (e) Between 1 and 1 of a revolution
4 2
(f) One complete revolution
Sol. (i) → (c); (ii) → (d); (iii) → (a); (iv) → (e); (v) → (b)
Ex 2. Just by observing/looking, identify the following angles as an acute angle, a right angle, a straight
angle, an obtuse angle or a reflex angle:
(a) (b) (c)

(d) (e) (f)

Lines and Angles 47