Step-by-step explanation:
Certainly! To fill in the sizes of each angle in a diagram using the properties of adjacent angles, vertically opposite angles, and corresponding angles, you'll need to follow these principles:
1. **Adjacent Angles**: Angles that share a common side and a common vertex, and don't overlap. The sum of adjacent angles forming a straight line is $180^\circ$.
2. **Vertically Opposite Angles**: When two lines intersect, the angles directly across from each other are called vertically opposite angles. These angles are equal.
3. **Corresponding Angles**: In the case of two parallel lines intersected by a transversal, corresponding angles are in the same relative position at each intersection. They are equal in measure.
Without the specific diagram, I can't provide the exact angle measurements, but here's an example of how you might apply these properties:
```
Given:
- Line AB is parallel to line CD.
- Line EF is a transversal intersecting both lines at points G and H.
- Angle AGH is given as 50°.
Find:
- The size of angle EGH, angle CGH, and angle CHD.
Solution:
- Angle AGH and angle EGH are corresponding angles, so angle EGH = 50°.
- Angle AGH and angle CGH are vertically opposite angles, so angle CGH = 50°.
- Angle CGH and angle CHD are adjacent angles forming a straight line, so angle CHD = 180° - 50° = 130°.
```
If you have a specific diagram, please describe it or share it, and I can help you calculate the angles based on the properties mentioned. Remember, the sum of angles around a point is $360^\circ$, and the sum of angles in a triangle is $180^\circ$. These additional properties may also be helpful in solving for unknown angles.
