in each figure, calculate the value of x.
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in each figure, calculate the value of x.
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To calculate the value of x in each figure, we can use the following steps:
1. Identify the type of angle or angles that are marked in the figure.
2. Use the appropriate geometric properties to find the values of the missing angles.
3. Substitute the values of the known angles into the equation to find the value of x.
**Figure 1**
This figure shows a supplementary angle. Supplementary angles add up to 180 degrees. Therefore, we have the following equation:
```
110 + x = 180
```
Subtracting 110 from both sides, we get:
```
x = 180 - 110
```
Therefore, x = **70 degrees**.
**Figure 2**
This figure shows two vertical angles. Vertical angles are equal to each other. Therefore, we have the following equation:
```
x = 122 degrees
```
Therefore, x = **122 degrees**.
**Figure 3**
This figure shows a triangle. The sum of the angles in a triangle is 180 degrees. Therefore, we have the following equation:
```
x + 60 + 105 = 180
```
Combining like terms, we get:
```
x + 165 = 180
```
Subtracting 165 from both sides, we get:
```
x = 180 - 165
```
Therefore, x = **15 degrees**.
**Figure 4**
This figure shows a quadrilateral. The sum of the angles in a quadrilateral is 360 degrees. Therefore, we have the following equation:
```
110 + 88 + 92 + x = 360
```
Combining like terms, we get:
```
290 + x = 360
```
Subtracting 290 from both sides, we get:
```
x = 360 - 290
```
Therefore, x = **70 degrees**.
**Figure 5**
This figure shows a pentagon. The sum of the angles in a pentagon is 540 degrees. Therefore, we have the following equation:
```
125 + 75 + 75 + 105 + x = 540
```
Combining like terms, we get:
```
380 + x = 540
```
Subtracting 380 from both sides, we get:
```
x = 540 - 380
```
Therefore, x = **160 degrees**.
**Figure 6**
This figure shows a hexagon. The sum of the angles in a hexagon is 720 degrees. Therefore, we have the following equation:
```
130 + 38 + 122 + 25 + 110 + x = 720
```
Combining like terms, we get:
```
425 + x = 720
```
Subtracting 425 from both sides, we get:
```
x = 720 - 425
```
Therefore, x = **295 degrees**.
**Conclusion**
The values of x in each figure are as follows:
* Figure 1: 70 degrees
* Figure 2: 122 degrees
* Figure 3: 15 degrees
* Figure 4: 70 degrees
* Figure 5: 160 degrees
* Figure 6: 295 degrees