Answer :
The pair of angles in the figures and the names of the angles, including the vertical angles are as follows;
1. Adjacent angles
2. Vertical angles
3. Adjacent angles
4. Linear pair angles
5. Adjacent angles
6. Linear pair angles
7. Vertical angles
8. Complementary angles
9. Supplementary angles
10. ∠EGF and ∠CGD
11. ∠BGF and ∠DGE
12. ∠BGC and ∠CGD
13. ∠CGD and ∠DGE
14. ∠AGB and ∠BGC
15. ∠DGE
What are vertical angles?
Vertical angles are the angles opposite each other when two lines intersect. They are always equal.
The definitions of the types of angle pairs and the names of the angles are as follows:
- Adjacent Angles: These are two angles that have a common vertex and a common side but do not overlap. In other words, they are next to each other.
- Vertical Angles: These are the angles opposite each other when two lines cross. They are always equal.
- Complementary Angles: These are two angles whose measures add up to 90 degrees. They don’t have to be next to each other.
- Supplementary Angles: These are two angles whose measures add up to 180 degrees. Like complementary angles, they don’t have to be adjacent.
- Linear Pair: This is a pair of adjacent angles formed when two lines intersect. In other words, they add up to 180 degrees and are therefore supplementary
The key characteristic of vertical angles is that they are always equal, regardless of whether they are acute or obtuse.
- Acute vertical angles are a pair of vertical angles where each angle measures less than 90 degrees. Since vertical angles are equal, if one angle is acute (< 90 degrees), then the other angle is also acute.
- Obtuse vertical angles are a pair of vertical angles where each angle measures more than 90 degrees but less than 180 degrees. Similarly, if one angle is obtuse (> 90 degrees and < 180 degrees), then the other angle is also obtuse.
- Two angles are said to be supplementary when the sum of their measures is 180 degrees. So, if you have one angle, the supplementary angle would be calculated as 180 degrees minus the measure of the known angle
Learn more on vertical angles here: https://brainly.com/question/4282601
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