Question

10
m∠a = 180°
is this angle acute, right, obtuse, or straight?
m∠a = 124°
is this angle acute, right, obtuse, or straight?
m∠a = 90°
is this angle acute, right, obtuse, or straight?
m∠a = 45°
is this angle acute, right, obtuse, or straight?

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

• For \(m\angle A=180^{\circ}\), since \(180^{\circ}\) matches the definition of a straight angle.
• For \(m\angle A = 124^{\circ}\), since \(90^{\circ}<124^{\circ}<180^{\circ}\), it is an obtuse angle.
• For \(m\angle A=90^{\circ}\), it is a right angle.
• For \(m\angle A = 45^{\circ}\), since \(0^{\circ}<45^{\circ}<90^{\circ}\), it is an acute angle.

Answer:

• \(m\angle A = 180^{\circ}\): Straight angle
• \(m\angle A=124^{\circ}\): Obtuse angle
• \(m\angle A = 90^{\circ}\): Right angle
• \(m\angle A=45^{\circ}\): Acute angle