CHECK IF THE GIVEN ANGLE IS IN STANDARD POSITION

An angle is said to be an angle in standard position if its vertex is at the origin of a coordinate grid and its initial arm coincides with the positive x-axis.

The position of an angle when its initial arm is  on the positive x-axis and its vertex is at the origin.

Example 1 : 

Is the following angle, θ, in standard position ?

Solution :

In the picture given above the angle is not in the standard position. 

Explanation :

The vertex of initial arm and terminal arm is not at origin.

Example 2 : 

Is the following angle, θ, in standard position ?

Solution :

In the picture given above the angle is in the standard position. 

Explanation :

The vertex is at origin and initial arm is in x axis. Hence the given angle is in standard position.

Example 3 : 

Is the following angle, θ, in standard position ?

Solution :

In the picture given above the angle is not in the standard position. 

Explanation :

The initial arm is not on the x-axis.

Example 4 :

Is the following angle, θ, in standard position ?

Solution :

In the picture given above the angle is in the standard position. 

Explanation :

The vertex is at origin and initial arm is in x axis. Hence the given angle is in standard position.

Example 5 :

Without measuring, match each angle with a diagram of the angle in standard position.

(a) 150°     (b) 180°      (c) 45°     (d) 320°

(e) 215°     (f) 270°

Solution :

(a)  150 

It is greater than 90 but lesser than 180.The picture F represents angle 150.

(b)  Picture C represents 180 degree.

(c)  45

45 degree is greater than 0 but lesser than 90. Picture A represents 45 degree.

(d)  320

320 degree is greater than 270 and lesser than 360. Picture D represents 320 degree.

(e)  215

215 is greater than 180 but lesser than 270, picture B represents 215.

(f)  270

Picture F represents 270 degree.

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