Types of Angles

When two rays share a common point, and angle is formed. The different types of angles are given in the image below.

Geometrical Properties

The following states some geometrical rules of angles. IMPT: When solving problems, do quote the bracket as stated beside each rule when using the property!
1. Complementary angles: Two angles are complementary if their sum adds up to 90°.
2. Supplementary angles: Two angles are supplementary if their sum adds up to 180°.
3. The sum of adjacent angles on a straight line is = 180°. (adj. ∠s on a straight line)
4. Angles at a point add up to 360. (∠s at a point)
5. Vertically opposite angles are equal. (vert. opp. ∠s)
6. For angles formed by parallel lines cut by a transversal, l, with reference to the picture shown below, 
(a) Corresponding angles are equal. a = b, (corr. ∠s, AB // CD)
(b) Alternate angles are equal. c = d, (alt. ∠s, AB // CD)
(c) Interior angles are supplementary. b + d = 180° (int. ∠s, AB // CD)

Perpendicular Bisector of a Line

The perpendicular bisector of a line segment forms a right angle with the line segment and divides the line segment into two equal parts. 
In the image below, PQ is called the perpendicular bisector of AB. Any point on the perpendicular bisector PQ is equidistant from the points A and B. 

Angle Bisector

An angle bisector is a ray that divides an angle into two equal angles. From the below image, if BX splits ∠ABC into two angles such that ∠ABX = ∠CBX, then BX is the angle bisector of ∠ABC.