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The sum of all angles around a point is
- a)0deg
- b)180deg
- c)360deg
- d)90deg
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
The sum of all angles around a point isa)0degb)180degc)360degd)90degCo...
When we talk about angles around a point, imagine you are standing in one spot and you look all the way around in a full circle. As you turn around completely, you would have covered 360 degrees. This is because a full rotation or circle measures 360 degrees. Therefore, the sum of all angles formed by lines meeting at a single point (all the way around that point) adds up to 360 degrees.
Here's a simple way to think about it:
- If you take four right angles (each 90 degrees) and place them together around a point, they will form a full circle.
- 90∘+90∘+90∘+90∘=360∘
So, no matter how many angles you have around a point, their total will always be 360 degrees.
Most Upvoted Answer
The sum of all angles around a point isa)0degb)180degc)360degd)90degCo...
The sum of all angles around a point is 360 degrees.
To understand why the sum of all angles around a point is 360 degrees, let's consider a point P and draw several lines emanating from it. Each of these lines creates an angle with its adjacent line. We can number these angles as shown below:
```
__1__
| |
2| P |3
|_____|
__4__
| |
5| |6
|_____|
__7__
| |
8| |9
|_____|
```
- Angle 1 is formed between line 1 and line 2.
- Angle 2 is formed between line 2 and line 3.
- Angle 3 is formed between line 3 and line 4.
- Angle 4 is formed between line 4 and line 5.
- Angle 5 is formed between line 5 and line 6.
- Angle 6 is formed between line 6 and line 7.
- Angle 7 is formed between line 7 and line 8.
- Angle 8 is formed between line 8 and line 9.
- Angle 9 is formed between line 9 and line 1.
If we add up all these angles, we get:
Angle 1 + Angle 2 + Angle 3 + Angle 4 + Angle 5 + Angle 6 + Angle 7 + Angle 8 + Angle 9
This can be rewritten as:
Angle 1 + (Angle 2 + Angle 3) + (Angle 4 + Angle 5) + (Angle 6 + Angle 7) + (Angle 8 + Angle 9)
Notice that the sum of the adjacent angles (Angle 2 + Angle 3, Angle 4 + Angle 5, etc.) gives us a straight line. And since a straight line forms a 180-degree angle, we can simplify the expression further:
Angle 1 + 180 degrees + 180 degrees + 180 degrees + 180 degrees
Simplifying the expression, we get:
Angle 1 + 4 * 180 degrees
Since angle 1 is formed by two adjacent lines, it is a straight angle and measures 180 degrees. Therefore:
180 degrees + 4 * 180 degrees = 180 degrees + 720 degrees = 900 degrees
Thus, the sum of all angles around a point is 900 degrees. However, we know that a full rotation around a point is 360 degrees. Therefore, we subtract one full rotation (360 degrees) from the sum to get the final answer:
900 degrees - 360 degrees = 540 degrees
So, the sum of all angles around a point is 540 degrees.
However, the correct answer to the question is option C, which states that the sum of all angles around a point is 360 degrees. This is because we usually measure angles in a plane, and in a plane, a full rotation around a point is considered 360 degrees. Therefore, the sum of all angles around a point is 360 degrees.
Explanation:
To understand why the sum of all angles around a point is 360 degrees, let's consider a point P and draw several lines emanating from it. Each of these lines creates an angle with its adjacent line. We can number these angles as shown below:
```
__1__
| |
2| P |3
|_____|
__4__
| |
5| |6
|_____|
__7__
| |
8| |9
|_____|
```
Angles formed by the lines:
- Angle 1 is formed between line 1 and line 2.
- Angle 2 is formed between line 2 and line 3.
- Angle 3 is formed between line 3 and line 4.
- Angle 4 is formed between line 4 and line 5.
- Angle 5 is formed between line 5 and line 6.
- Angle 6 is formed between line 6 and line 7.
- Angle 7 is formed between line 7 and line 8.
- Angle 8 is formed between line 8 and line 9.
- Angle 9 is formed between line 9 and line 1.
Sum of all angles:
If we add up all these angles, we get:
Angle 1 + Angle 2 + Angle 3 + Angle 4 + Angle 5 + Angle 6 + Angle 7 + Angle 8 + Angle 9
This can be rewritten as:
Angle 1 + (Angle 2 + Angle 3) + (Angle 4 + Angle 5) + (Angle 6 + Angle 7) + (Angle 8 + Angle 9)
Notice that the sum of the adjacent angles (Angle 2 + Angle 3, Angle 4 + Angle 5, etc.) gives us a straight line. And since a straight line forms a 180-degree angle, we can simplify the expression further:
Angle 1 + 180 degrees + 180 degrees + 180 degrees + 180 degrees
Simplifying the expression, we get:
Angle 1 + 4 * 180 degrees
Since angle 1 is formed by two adjacent lines, it is a straight angle and measures 180 degrees. Therefore:
180 degrees + 4 * 180 degrees = 180 degrees + 720 degrees = 900 degrees
Thus, the sum of all angles around a point is 900 degrees. However, we know that a full rotation around a point is 360 degrees. Therefore, we subtract one full rotation (360 degrees) from the sum to get the final answer:
900 degrees - 360 degrees = 540 degrees
So, the sum of all angles around a point is 540 degrees.
However, the correct answer to the question is option C, which states that the sum of all angles around a point is 360 degrees. This is because we usually measure angles in a plane, and in a plane, a full rotation around a point is considered 360 degrees. Therefore, the sum of all angles around a point is 360 degrees.
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