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Classification of Angles : Adjacent Angles

Adjacent Angles

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.

Classification of angles

  • is the common vertex
  • $A\hat{O}B$ and $B\hat{O}C$ are adjacent angles.
  • Arm BO separates the two angles.

Complementary Angles

If the sum of the two angles is one right angle (i.e., 90o), they are called complementary angles.

If the measure of $A\hat{O}C$ = a0 , $C\hat{O}B$ = b0 , then a0 + b0 = 900 .

Therefore $A\hat{O}C$ and $C\hat{O}B$ are complementary angles.

$A\hat{O}C$ is complement of $C\hat{O}B$

Classification of angles

Supplementary Angles

Two angles are said to be supplementary, if the sum of their measures is 180o.

Example

Angles measuring 130o and 50o are supplementary angles.

Two supplementary angles are the supplement of each other.

Classification of angles

Vertically Opposite Angles

When two straight lines intersect each other at a point, the pairs of opposite angles so formed are called vertically opposite angles.

Classification of angles

Angles $\angle{1}$ and $\angle{3}$ and angles $\angle{2}$ and $\angle{4}$ are vertically opposite angles. Vertically opposite angles are always equal.

Bisector of an Angle

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.

Classification of angles

$B\hat{O}C$ = $C\hat{O}A$

And $B\hat{O}C$ + $C\hat{O}A$ = $A\hat{O}B$

And $A\hat{O}B$ = 2$B\hat{O}C$ = 2$C\hat{O}A$