Triangle Angle Calculator

Triangle Angle

Find the third angle of a triangle

Geometric Fact

The sum of all interior angles in a triangle is always 180 degrees.

How to Find the Third Angle

Step 1: Identify the Known Angles

Write down the two known angles A and B in degrees.

Why: You need exactly two angles to find the third. Make sure your values are clearly recorded.

Step 2: Verify Angles Are Valid

Check that both angles are positive and each is less than 180 degrees.

Why: Triangle angles must each be between 0° and 180°. Negative or excessive values indicate measurement errors.

Step 3: Check Sum of Two Angles

Verify that A + B is less than 180 degrees.

Why: If A + B ≥ 180°, there's no room for angle C. This catches impossible triangles before calculation.

Step 4: Calculate the Third Angle

Apply the formula: C = 180 - A - B

Why: This formula derives from the geometric fact that all interior angles in any triangle sum to 180 degrees.

Step 5: Verify the Result

Check that C is positive and that A + B + C = 180 exactly.

Why: This verification confirms the calculation is correct and the triangle is geometrically valid.

Real-World Example

Surveying a Triangular Plot

Scenario: A surveyor measures two angles of a triangular land plot: 65° and 52°. What is the third angle?
Step 1: Known angles: A = 65°, B = 52°
Step 2: Both positive ✓, both less than 180° ✓
Step 3: Sum check: 65 + 52 = 117° < 180° ✓
Step 4: C = 180 - 65 - 52 = 63°
Step 5: Verify: 65 + 52 + 63 = 180° ✓
Verification: Sum check: 180 - 117 = 63°; Total = 180° exact
Result: The third angle is 63 degrees
Interpretation: The survey now has all three angles: 65°, 52°, and 63°. This helps establish the plot's geometric properties for legal documentation and construction planning.

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