Angles
Angles are made when corners are formed.
Below we have an image of a box with its lid partially lifted. It can be seen that the edges AD and AP can be extended upto points DEx and PEx,respectively and imagined as two rays ADEx and APEx. These two rays have a common initial point A.
The two rays here together are said to form an angle.
An angle is made up of two rays starting from a common initial point.
The two rays forming the angle are called the arms or sides of the angle. The common initial point is the vertex of the angle.
Angle subtended by rays OP and OQ (∠POQ)
Above we have an angle formed by rays OP and OQ. To show this we use a small curve at the vertex. O is the vertex.
What about the sides? Are they OP and OQ or not ? How to name the angle?
It is simply, an angle at O. We can be more specify by identifying a point on either "arms" and including the vertex in the middle to name the angle. Angle POQ (∠POQ) is the mathematical name of the said the angle.
When specifying the angle, the vertex is always written as the middle letter as a convention.
Interior of an Angle
Angle∠ABC
One shade
Both shades
Randomly, make two intersecting rays on paper. Say, the angle is ∠ABC with B as the common vertex.
Now, shade the region that is bordered by AB and where BC also lies.
Next, shade the portion bordering BC and where BA lies, with a different colour.
The portion common to both shadings is called the interior of ∠ABC.
The interior is not a restricted area here, as it extends indefinitely. (Both BA and CB are rays)
Solve
Draw diagram of two angles such that they have :
(a) One point in common.
What is the common point among the adjacent angles shown in the figure?
(b) Two points in common.
What are the two common points among the adjacent angles shown in the figure?