What does it mean (180⁰ - θ)?

[Indranil]

Suppose angles between two vectors A and B is θ. Then angles between A and -B will be 180⁰ - θ.
What does it mean (180⁰ - θ)? Does it mean 180⁰ or less than 180⁰?

 

[MarkFL]

Consider the following diagram:



The vectors \(\displaystyle \vec{B}\) and \(\displaystyle -\vec{B}\) simply form a line segment, and the angles \(\displaystyle \theta\) and \(\displaystyle 180^{\circ}-\theta\) are supplemental, meaning their sum is \(\displaystyle 180^{\circ}\).

 

[Indranil]

Consider the following diagram:

View attachment 9755

The vectors \(\displaystyle \vec{B}\) and \(\displaystyle -\vec{B}\) simply form a line segment, and the angles \(\displaystyle \theta\) and \(\displaystyle 180^{\circ}-\theta\) are supplemental, meaning their sum is \(\displaystyle 180^{\circ}\).

You said their sum, so how to add them like, sum = 180-θ + θ = 180⁰.

 

[MarkFL]

You said their sum, so how to add them like, sum = 180-θ + θ = 180⁰.

Yes, exactly.

 

[mmm4444bot]

What does it mean (180⁰ - θ)?

It is the difference between two angle measurements (180° and θ).

Does it mean 180⁰

Only when θ = 0°

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180° = 1/2 revolution.

Example: You want 1/2 revolution. You rotate θ degrees, and that is less than 1/2 revolution. How much more rotation do you need?

The answer is 180° - θ

 

[Indranil]

A and B vectors, the angle is θ, A and -B vectors, why angle is 180⁰-θ?

A and B vectors, the angle is θ, A and -B vectors, why the angle is 180⁰-θ? Could you simplify it, please?

 

[lev888]

The angles are supplementary (thanks, Dr.Peterson).

 

[Indranil]

A and B vectors, the angle is θ, A and -B vectors, why the angle is 180⁰-θ? Could you simplify it, please?

I have three questions
1.'α' is what degree?
2.'β' is what degree?
3. What does '180⁰-θ' mean here? Please explain

 

[Dr.Peterson]

I have three questions
1.'α' is what degree?
2.'β' is what degree?
3. What does '180⁰-θ' mean here? Please explain

I think lev888 meant that the angles are supplementary, meaning that their sum is 180°.

Angles alpha and beta are not relevant to your question; perhaps they are used later in the solution being shown. You can't calculate them knowing only theta.

All we know, given what you have shown, is that the sum α+β is equal to 180°-θ. That is because that angle is supplementary to the given angle θ, since vector A divides the straight angle formed by B and -B into two parts, which add up to a straight angle (180°).

One could say that 180°-θ means that we are taking angle θ away from that straight angle, and 180°-θ is what remains. That is, it is a subtraction.

In the future, please check whether your picture is clear before submitting. This is horribly fuzzy.

 

[MarkFL]

I guess you didn't see my reply the first time you posted this same question...