Question

teacher :
classify each angle as acute, obtuse, right, or straight.
1)
2)
3)
4)
5)
6)
7)
8)
9)
10)

1. 93°
2. 116°
3. 31°
4. 9°
5. 90°
6. 98°
7. 94°
8. 24°
9. 180°
10. 8°

Explanation:

Step1: Recall angle definitions

• Acute angle: \(0^{\circ}<\theta < 90^{\circ}\)
• Right angle: \(\theta = 90^{\circ}\)
• Obtuse angle: \(90^{\circ}<\theta < 180^{\circ}\)
• Straight angle: \(\theta = 180^{\circ}\)

Step2: Classify each angle

1. For \(93^{\circ}\): \(90^{\circ}<93^{\circ}<180^{\circ}\), so it is obtuse.
2. For \(116^{\circ}\): \(90^{\circ}<116^{\circ}<180^{\circ}\), so it is obtuse.
3. For \(31^{\circ}\): \(0^{\circ}<31^{\circ}<90^{\circ}\), so it is acute.
4. For \(9^{\circ}\): \(0^{\circ}<9^{\circ}<90^{\circ}\), so it is acute.
5. For \(90^{\circ}\): \(\theta = 90^{\circ}\), so it is right.
6. For \(98^{\circ}\): \(90^{\circ}<98^{\circ}<180^{\circ}\), so it is obtuse.
7. For \(94^{\circ}\): \(90^{\circ}<94^{\circ}<180^{\circ}\), so it is obtuse.
8. For \(24^{\circ}\): \(0^{\circ}<24^{\circ}<90^{\circ}\), so it is acute.
9. For \(180^{\circ}\): \(\theta = 180^{\circ}\), so it is straight.
10. For \(8^{\circ}\): \(0^{\circ}<8^{\circ}<90^{\circ}\), so it is acute.

Answer:

1. Obtuse
2. Obtuse
3. Acute
4. Acute
5. Right
6. Obtuse
7. Obtuse
8. Acute
9. Straight
10. Acute