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| Measurement of Angles |
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| To measure an angle we shall use two kinds of units, the degree unit and the radian unit. |
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A degree is defined to be an angle formed by half-line (or a ray)
rotated about its end point  of
a complete revolution. |
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| To denote degree measure we use the symbol (o), written just to the right of measure number of the angle. |
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| Thus 360o = 1 complete rotation |
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| The number of degrees in the circumference of the circle between the initial and terminal sides of the angle is its degree measure. |
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| 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 ("). |
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| 1o = 60 minutes = 60' |
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| 1' = 60 seconds = 60" |
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| \ 1o = 3600" |
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| Thus 49 degrees 38 minutes 56 seconds is written in symbols as |
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| 49o 38' 56" |
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| Note:
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| i) Angle 0o: If there is no rotation, ie., the initial side and the terminating side of the angle coincides then the angle measure is 0o. |
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| 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 |
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| The measure of the angle forms = [(360)(2) + 60]o = 780o |
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| Acute angle |
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| An angle whose measure is less than 90o. (0 < q < 90) |
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| Obtuse angle |
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| An angle whose measure is grater than 90o but less than 180o. (90o< q < 180o) |
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| Right angle |
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| An angle whose measure is 90o. (q = 90o) |
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| Reflex angle |
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| An angle whose measure is greater than 180o but less than 360o. (180o< q < 360o) |
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| A straight angle |
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| An angle whose measure is 180o. |
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