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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