1. Complementary angles: Two angles whose sum is equal to \(\mathbf{90}°.\)
In the above figure, \(\angle1\ and\ \angle2\) are complementary angles because these are two parts of an angle of \(\mathbf{90}°\) (right angle); by combining (or adding) these two, we will get a \(\mathbf{90}°\) angle.
2. Supplementary angles: Two angles whose sum is equal to \(\mathbf{180}°\).
In the above figure, \(\angle1\ and\ \angle2\) are Supplementary angles because these are two parts of an angle of \(\mathbf{180}°\) (straight angle); by combining (or adding) these two, we will get a \(\mathbf{180}°\) angle. Supplementary angles are also known as ‘Linear Pair of angles’.
3. Vertical opposite angles: there are four (4) angles between two (2) intersecting lines, and angles opposite to each other are called vertical opposite angles and vertical opposite angles are always equal.
In the above figure,\ \(\angle\mathbf{1}=\angle\mathbf{4}\) and \(\angle\mathbf{2}=\angle\mathbf{3}\); because these are opposite to each other.
4. Angles between parallel lines:
(a) Alternate Interior Angles: The angles in the interior (between) of two parallel lines and also on the opposite sides (alternate sides) of an intersecting line, are called alternate interior angles and Alternate interior angles are always equal.
In the above 3 figures ; \(\angle\mathbf{1}=\angle\mathbf{4}\) and ; \(\angle\mathbf{2}=\angle\mathbf{3}\); because they are on opposite sides of the intersecting line (left and right) and they are between the same parallel lines.
(b) Alternate Exterior Angles: The angles in the exterior (outside) of two parallel lines and also on the opposite sides (alternate sides) of an intersecting line, are called alternate exterior angles and Alternate exterior angles are always equal.
In the above 3 figures ; \(\angle\mathbf{1}=\angle\mathbf{4}\) and ; \(\angle\mathbf{2}=\angle\mathbf{3}\); because they are on opposite sides of the intersecting line (left and right) and they are outside the same parallel lines.
(c) Corresponding Angles: Two angles formed on the same side on an intersecting line and one must be interior and other exterior of a pair of parallel lines are called corresponding angles and corresponding angles are always equal if they are formed with parallel lines.
In the above 3 figures ; \(\angle\mathbf{1}=\angle\mathbf{5}\), \(\angle\mathbf{2}=\angle\mathbf{6},\ \angle\mathbf{3}=\angle\mathbf{7}\ {and}\ \angle\mathbf{4}=\angle\mathbf{8}\) because they are on the same side of the intersecting line (left or right) and one of each pair is outside (exterior) and other is inside (interior) of the same parallel lines.
(d) Interior angles on the same side of an intersecting line: The angles in the interior of two parallel lines and on the same side of an intersecting line.
In the above 3 figures; \(\angle\mathbf{1}\ {and}\ \angle\mathbf{3}\ ;\ \ \ \angle\mathbf{2}\ {and}\ \angle\mathbf{4}\) are interior angles on the same side of an intersecting line.
Note: When the lines are parallel, the interior angles on the same side of the intersecting line, are supplementary.
To learn about some other types of angles, click Here