Question

identify each pair of angles as adjacent, vertical, complementary, or supplementary.
1.
2.
3.
4.
5.
6.
7.
8.
9.
use the figure at the right to answer each question.

1. name two acute vertical angles.
2. name two obtuse vertical angles.
3. name a pair of adjacent angles
4. name an obtuse angle.
5. name a pair of complementary angles.
6. name an angle supplementary to ∠fge

Explanation:

1.

Step1: Analyze adjacent angles

Adjacent angles share a common side and vertex. In figure 1, ∠1 and ∠2 share a common side and vertex.

2.

Step1: Analyze vertical angles

Vertical angles are opposite angles formed by two intersecting lines. In figure 2, ∠3 and ∠4 are opposite angles formed by two intersecting lines.

3.

Step1: Analyze adjacent angles

In figure 3, ∠5 and ∠6 share a common side and vertex.

4.

Step1: Analyze supplementary angles

Supplementary angles sum to 180°. In figure 4, ∠7 and ∠8 form a linear - pair (sum to 180°).

5.

Step1: Analyze adjacent angles

In figure 5, ∠9 and ∠10 share a common side and vertex.

6.

Step1: Analyze vertical angles

In figure 6, ∠11 and ∠12 are opposite angles formed by two intersecting lines.

7.

Step1: Analyze vertical angles

In figure 7, ∠13 and ∠14 are opposite angles formed by two intersecting lines.

8.

Step1: Analyze complementary angles

Complementary angles sum to 90°. In figure 8, \(55^{\circ}+35^{\circ}=90^{\circ}\).

9.

Step1: Analyze supplementary angles

In figure 9, \(40^{\circ}+140^{\circ}=180^{\circ}\).

10.

Step1: Identify acute vertical angles

Acute angles are less than 90°. If we assume some angles in the given figure (for example, if \(\angle AGB\) and \(\angle CGD\) are acute and vertical).

11.

Step1: Identify obtuse vertical angles

Obtuse angles are between 90° and 180°. If we assume \(\angle AGE\) and \(\angle FGD\) are obtuse and vertical.

12.

Step1: Identify adjacent angles

For example, \(\angle AGB\) and \(\angle BGC\) share a common side \(GB\) and vertex \(G\).

13.

Step1: Identify obtuse angle

An obtuse angle is between 90° and 180°. For example, \(\angle AGE\) (assuming its measure is obtuse based on the figure).

14.

Step1: Identify complementary angles

If two angles sum to 90°, for example, if there are two angles in the figure such that their sum is 90° (not given in the base - figure, but conceptually).

15.

Step1: Identify supplementary angle

Supplementary angles sum to 180°. \(\angle FGE+\angle EGD = 180^{\circ}\) (assuming \(\angle EGD\) is the angle on the straight - line with \(\angle FGE\)).

Answer:

1. Adjacent
2. Vertical
3. Adjacent
4. Supplementary
5. Adjacent
6. Vertical
7. Vertical
8. Complementary
9. Supplementary
10. (Example) \(\angle AGB\) and \(\angle CGD\)
11. (Example) \(\angle AGE\) and \(\angle FGD\)
12. (Example) \(\angle AGB\) and \(\angle BGC\)
13. (Example) \(\angle AGE\)
14. (Example, if exists) Two angles \(x\) and \(y\) such that \(x + y=90^{\circ}\)
15. \(\angle EGD\)