To classify each of the given angles as 'acute', 'obtuse', 'right', or 'straight', we use the following criteria:
- An acute angle is less than [tex]\(90^\circ\)[/tex].
- A right angle is exactly [tex]\(90^\circ\)[/tex].
- An obtuse angle is greater than [tex]\(90^\circ\)[/tex] but less than [tex]\(180^\circ\)[/tex].
- A straight angle is exactly [tex]\(180^\circ\)[/tex].
Let's classify each angle step-by-step:
1. [tex]\(68^\circ\)[/tex]: Since [tex]\(68 < 90\)[/tex], it is an acute angle.
2. [tex]\(177^\circ\)[/tex]: Since [tex]\(90 < 177 < 180\)[/tex], it is an obtuse angle.
3. [tex]\(131^\circ\)[/tex]: Since [tex]\(90 < 131 < 180\)[/tex], it is an obtuse angle.
4. [tex]\(15^\circ\)[/tex]: Since [tex]\(15 < 90\)[/tex], it is an acute angle.
5. [tex]\(162^\circ\)[/tex]: Since [tex]\(90 < 162 < 180\)[/tex], it is an obtuse angle.
6. [tex]\(32^\circ\)[/tex]: Since [tex]\(32 < 90\)[/tex], it is an acute angle.
7. [tex]\(90^\circ\)[/tex]: Since it is exactly [tex]\(90^\circ\)[/tex], it is a right angle.
8. [tex]\(135^\circ\)[/tex]: Since [tex]\(90 < 135 < 180\)[/tex], it is an obtuse angle.
9. [tex]\(49^\circ\)[/tex]: Since [tex]\(49 < 90\)[/tex], it is an acute angle.
10. [tex]\(90^\circ\)[/tex]: Since it is exactly [tex]\(90^\circ\)[/tex], it is a right angle.
11. [tex]\(180^\circ\)[/tex]: Since it is exactly [tex]\(180^\circ\)[/tex], it is a straight angle.
12. [tex]\(175^\circ\)[/tex]: Since [tex]\(90 < 175 < 180\)[/tex], it is an obtuse angle.
13. [tex]\(48^\circ\)[/tex]: Since [tex]\(48 < 90\)[/tex], it is an acute angle.
14. [tex]\(20^\circ\)[/tex]: Since [tex]\(20 < 90\)[/tex], it is an acute angle.
15. [tex]\(64^\circ\)[/tex]: Since [tex]\(64 < 90\)[/tex], it is an acute angle.
16. [tex]\(180^\circ\)[/tex]: Since it is exactly [tex]\(180^\circ\)[/tex], it is a straight angle.
17. [tex]\(157^\circ\)[/tex]: Since [tex]\(90 < 157 < 180\)[/tex], it is an obtuse angle.
18. [tex]\(7^\circ\)[/tex]: Since [tex]\(7 < 90\)[/tex], it is an acute angle.
19. [tex]\(8^\circ\)[/tex]: Since [tex]\(8 < 90\)[/tex], it is an acute angle.
20. [tex]\(92^\circ\)[/tex]: Since [tex]\(90 < 92 < 180\)[/tex], it is an obtuse angle.
Therefore, the classifications are as follows:
1. Acute
2. Obtuse
3. Obtuse
4. Acute
5. Obtuse
6. Acute
7. Right
8. Obtuse
9. Acute
10. Right
11. Straight
12. Obtuse
13. Acute
14. Acute
15. Acute
16. Straight
17. Obtuse
18. Acute
19. Acute
20. Obtuse
