1. What is an Obtuse Angle in a Triangle?

Definition: An obtuse angle is any angle greater than 90 degrees in a triangle. A triangle can have at most one obtuse angle.

Purpose: Understanding angle types helps in triangle classification and solving geometric problems.

2. How Does the Calculator Work?

The calculator uses the triangle angle sum formula:

Where:

• Enter any two angles of a triangle
• The third angle is calculated automatically
• The calculator counts how many angles are obtuse (>90°) and acute (<90°)

3. Triangle Angle Rules

Key Facts:

• All triangles have exactly 180° when their angles are summed
• A triangle can have either:
  • Three acute angles (all <90°)
  • One right angle (90°) and two acute angles
  • One obtuse angle (>90°) and two acute angles
• It's impossible for a triangle to have more than one obtuse angle

4. Using the Calculator

Tips:

• Enter any two known angles of a triangle (in degrees)
• Values must be between 0 and 180
• The sum of two angles must be less than 180°
• The calculator will determine the third angle and classify all angles

5. Frequently Asked Questions (FAQ)

Q1: Can a triangle have two obtuse angles?
A: No, the sum would exceed 180° which is impossible in Euclidean geometry.

Q2: What's the difference between obtuse and acute angles?
A: Obtuse angles are >90°, acute angles are <90°, and right angles are exactly 90°.

Q3: What triangle has one obtuse angle?
A: An obtuse triangle has one angle >90° and two angles <90°.

Q4: Can all three angles be obtuse?
A: No, the sum would be >270° which violates the 180° rule.

Q5: What's the maximum possible obtuse angle in a triangle?
A: Just under 180° (e.g., 179.999° with two near-0° angles).