Lines and Angles
- Angle: An angle is the union of two rays with a common initial point. An angle is denoted by symbol\[\angle \]. It is measured in degrees,
The angle formed by the two rays \[\overline{AB}\,\,and\,\,\overline{AC}\text{ }is\text{ }\angle BAC\text{ }or\text{ }\angle CAB.~\]called \[\overline{AB}\,\,and\,\,\overline{AC}\]are called the arms and the common initial point ‘A’ is called the vertex of the angle.
- Bisector of an angle: A line which divides an angle into two equal a parts is alled the bisector of the angle.
e.g., In the adjacent figure, the line OP divides \[\angle \]AOB into two
Equal parts.
\[\angle AOP=\angle POB={{\operatorname{x}}^{o}}\]
So, the line OP is ‘called the bisector of \[\angle \]AOB.
(i) Complementary angles: Two angles are said to be Complementary if the sum of their measures is equal to\[~{{90}^{o}}\]
Here\[\angle x+\angle y={{90}^{o}},\]therefore \[\angle x\,\operatorname{and}\,\angle y\] Complementary angles:
(ii) Supplementary angles: Two angles are said to be supplementary if the sum of their measures isequal to\[{{180}^{o}}\].
Here \[\angle x+\angle y={{180}^{o}},\]therefore \[\angle x\,\operatorname{and}\,\angle y\]
Supplementary angles.
- Adjacent angles: Angles having the same vertex and a common arm, and the non-common arms lie on the opposite sides of the common arm are called adjacent angles.
- \[\angle AOB\text{ }and\text{ }\angle COB\]with common vertex 0 and common arm OB are adjacent angles,
Note: \[\angle AOC=\angle AOB+\angle BOC\]
- Linear pair of angles: Two adjacent angles make a linear pair of angles, if the non-common arms of these angles are two opposite rays (with same end point),
- In the adjacent figure, \[\angle BAC\text{ }and\text{ }\angle CAD\]form a linear pair of angles because the non -common arms AB and AD of the two angles are two opposite rays.
Moreover,\[\angle \text{ }BAC\text{ }+\text{ }\angle
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