Lines and Angles

Lines and Angles:

Suppose we have a ray OA on a plane with end point O. With the same plane end point. Consider another ray OB in the same plane. We observe that OB is obtained from OA through suitable rotation around  the point O. We say OB subtends an angle with angle OA. The amount of rotation is the measure of this angle.

∠AOB

We use numerical measurement called degree to measure angles. We use the notation to denote a degrees. The rays OA and OB are called the sides of the angle and O is called the vertex if the angle. The angle subtended by the rays OA and OB is denoted by ∠AOB.

We know a geometrical instrument called protractor which is used to measure the angles.

We Know, different types of angles:

Straight line angle, right angle, acute angle, obtuse angle, reflex angle, complete angle, adjacent angle, complementary angles and supplementary angles.

Let us recall one by one,

Two angles are said to be supplementary angles if their sum is 180˚. Similarly, two angles are said to be complementary if they add up to 90˚

Two angles are said to be adjacent angles, if both the angles have a common vertex and a common side.

While measuring the lengths are segments of the angles we observe the following rules:

Rule 1: Every line segment has a positive length. (The length of the line segment AB is denoted by AB or |AB|.)

Rule 2: If a point C lies on a line segment |AB|, then the length of |AB| is equal to the sum of the lengths of |AC| and |CB|; that is AB = AC + CB.

Rule 3: Every angles has a certain magnitude. A straight angles measures 180°

Rule 4: If OA, OB and OC are such that OC lies between OA and OB then ∠AOB = ∠AOC + ∠COB

Rule 5: If the angle between two rays is zero then they coincide. Conversely,  if two rays coincide, the angle between them is either zero or an integral multiple of 360°