Question

State true(T) or false (F):
The vertex of an angle lies in its interior.

Answer 1

Hint: In this question we have to check the position of the vertex of an angle. First we should know what an angle is. We know that an angle is a measurement between the two joining lines or rays which have a common intersecting point which represents the relations between the lines. We will draw a diagram and check whether the given statement is true or false.

Complete step-by-step answer:
Here we will first draw a clear diagram of the angle.

In the above figure we can see that $AB$ and $OB$ are two lines, which forms an angle $\angle AOB$.
We know from the definition that vertex is the point of angle which is the common point of the two lines or rays which forms an angle.
So here the vertex is point $O$. From the above figure we can see that the vertex $O$ neither lies in the interior nor the outside. It is on the angle.
Hence we can conclude that the above given statement in the question is false.
So, the correct answer is “False”.

Note: We should know that there are different parts in angle such as vertex, arms, initial side and terminal side. In the above figure the vertex is point $O$. The two ;lines or rays are known as arms. So in the above figure $OA$ and $OB$ are the arms. The definition of initial side says that it is the reference line which is based on the angle. So we have $OB$ as the initial side and the terminal side is the line or ray whose position is given by the angle with respect to the initial line. So the terminal side is $AB$.