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| Angles |
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| Definition |
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| When two straight lines meet at a point they form an angle. |
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 The point at which the arms meet (O) is known as the vertex of the angle. |
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 The amount of turning from one arm (OA) to other (OB) is called the
measure of the angle (ÐAOB) and written as m
ÐAOB. |
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| An angle is measured in degrees, minutes and seconds. |
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 If a ray rotates about the starting initial position, in anticlockwise direction, comes back to its original position after 1 complete revolution then it has rotated through 360o. |
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 1 complete rotation is divided into 360 equal parts. Each part is 1o. |
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| Each part (1o) is divided into 60 equal parts, each part measures one minute, written as 1'. |
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| 1' is divided into 60 equal parts, each part measures 1 second, written as 1". |
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| Degrees -----> minutes --------> seconds |
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| 1o = 60' |
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| Recall that the union of two rays forms an angle. |
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| In the figure, observe the different types of angles: |
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| Right angle |
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| An angle whose measure is 90o is called a right angle. |
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| Acute angle |
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| An angle whose measure is less then one right angle (i.e., less than 90o), is called an acute angle. |
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| Obtuse angle |
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| An angle whose measure is more than one right angle and less than two right angles (i.e., less than 180o and more than 90o) is called an obtuse angle. |
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| Straight angle |
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| An angle whose measure is 180o is called a straight angle. |
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| Reflex angle |
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| An angle whose measure is more than 180o and less than 360o is called a reflex angle. |
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| Complete angle |
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| An angle whose measure is 360o is called a complete angle. |
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| Equal angles |
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| Two angles are said to be equal, if they have the same measure. |
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| Adjacent angles |
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| Two angles having a common vertex and a common arm, such that the other arms of these angles are on opposite sides of the common arm, are called adjacent angles. |
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| Complementary angles |
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| If the sum of the two angles is one right angle (i.e., 90o), they are called complementary angles. |
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| Supplementary angles |
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| Two angles are said to be supplementary, if the sum of their measures is 180o. |
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| Example: |
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| Angles measuring 130o and 50o are supplementary angles. |
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| Two supplementary angles are the supplement of each other. |
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| Vertically opposite angles |
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| When two straight lines intersect each other at a point, the pairs of opposite angles so formed are called vertically opposite angles. |
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| Angles Ð1 and
Ð3 and angles Ð2 and
Ð4 are vertically opposite angles. |
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| Vertically opposite angles are always equal. |
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| Bisector of an angle |
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| If a ray or a straight line passing through the vertex of that angle, divides the angle into two angles of equal measurement, then that line is known as the Bisector of that angle. |
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| Linear pair of angles |
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| Two adjacent angles are said to form a linear pair of angles, if their non-common arms are two opposite rays. |
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| Recall adjacent angles. Now observe the pairs of angles in the figure. |
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