Measurement of Angles

Ask a Question, Get an Answer!

Type your question here

Hundreds of tutors are online and ready to help you right now!

To measure an angle we shall use two kinds of units, the degree unit and the radian unit.

Degree Measure (Sexagesimal system)

OR

A degree is defined to be an angle formed by half-line (or a ray) rotated about its end point of a complete revolution.

To denote degree measure we use the symbol (^o), written just to the right of measure number of the angle.

Thus 360^o = 1 complete rotation

The number of degrees in the circumference of the circle between the initial and terminal sides of the angle is its degree measure.

A degree is further divided into 60 equal part called a minutes and each minute is further subdivided into 60 equal parts called seconds, we denote the minute by (') and second by (").

1^o = 60 minutes = 60'

1' = 60 seconds = 60"

\ 1^o = 3600"

Thus 49 degrees 38 minutes 56 seconds is written in symbols as

49^o 38' 56"

Note:

i) Angle 0^o: If there is no rotation, ie., the initial side and the terminating side of the angle coincides then the angle measure is 0^o.

ii) If a radius vector makes a 'n' number of rotations and finally stops at a position then the angle is [(360)(n) + q]^o

The measure of the angle forms = [(360)(2) + 60]^o = 780^o

Types of Angles

Acute angle

An angle whose measure is less than 90^o. (0 < q < 90)

Obtuse angle

An angle whose measure is grater than 90^o but less than 180^o. (90^o< q < 180^o)

Right angle

An angle whose measure is 90^o. (q = 90^o)

Reflex angle

An angle whose measure is greater than 180^o but less than 360^o. (180^o< q < 360^o)

A straight angle

An angle whose measure is 180^o.