Pairs of Angles
Some angles are given special names due to their positions. They always appear in pairs. Such angles are called pairs of angles. In this section, you will study about the pairs of angles.
Adjacent Angles
Two angles in a plane are said to be adjacent angles if they have
a. a common vertex
b. a common arm and
c. both are on the opposite sides of the common arm.
Linear Pair of Angles
A pair of adjacent angles are said to form a linear pair if their exterior arms form a straight line, i.e. the sum of linear pair of angles is always 180°. Here, ∠XOY and ∠YOZ form a linear pair.
Angles at a Point
When many angles are formed at the same point, then they are called angles at a point.
Sum of all angles at a point is always 360°.
In the given figure, ∠1 + ∠2 + ∠3 + ∠4 + ∠5 = 360°.
Complementary Angles
If the sum of the measures of two angles is 90°, then the angles are said to be complementary angles.
In the following figures, ∠ABC + ∠PQR = 90°.
Therefore, ∠ABC and ∠PQR are complementary angles.
Each angle is said to be the complement of the other.
Supplementary Angles
If the sum of the measures of two angles is 180°, then the angles are said to be supplementary angles. Supplementary angles need not be adjacent angles.
In the following figures, ∠XYZ + ∠PQR = 180°.
Thus, ∠XYZ and ∠PQR are supplementary angles.
Each angle is said to be the supplement of the other.
Vertically Opposite Angles
When two lines p and q intersect each other at a point, they form four angles, say a, b, c and d. The opposite angles a and c are called vertically opposite angles, and so are opposite angles b and d.
