Angles on a straight line, intersecting lines

Complementary Angle: The sum of the measures of two angles is 90°
Supplementary Angle: The sum of the measures of two angles is 180°
Adjacent Angle: Adjacent angles have a common vertex and a common arm but no common interior points
Linear pair: A linear pair is a pair of adjacent angles whose non-common sides are opposite rays
Vertically Opposite Angles: when two lines intersect, the vertically opposite angles so formed are equal 
Pairs of Lines
Intersecting lines: Two lines intersect if they have a point in common. This common point O is their point of intersection.

Adjacent Angles
A pair of angles which are placed next to each other in such a way that they have a common vertex and an arm which is common to both the angles are called adjacent angles.

Linear Pair
A linear pair is a pair of adjacent angles whose non-common arms are opposite rays.
A pair of angles placed adjacent to each other is called a linear pair if the sum of their measures is 180°.

Note: A pair of supplementary angles form a linear pair when placed adjacent to each other.
When two lines intersect, the vertically opposite angles so formed are equal.

1 + 2 = 180° …(1)
1 and 2 form a linear pair
3 + 2 = 180° …(2)
3 and 2 form a linear pair

From (1) and (2)
1 = 3
Similarly, we can prove that
2 = 4

Intersecting Lines
Two lines intersect if they have a point in common called their point of intersection.