Find the missing angle in a triangle or verify whether three given angles form a valid triangle. The sum of interior angles always equals 180 degrees.
Triangle Angle Calculator - Find the Missing Angle
Find the missing angle in a triangle or verify whether three given angles form a valid triangle. The sum of interior angles always equals 180 degrees.
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Every triangle hides the same secret: 180 degrees
No matter how you stretch, squash, or rotate a triangle on a flat surface, its three interior angles always add up to exactly 180 degrees. This single rule is enough to find any missing angle when you know the other two, and to verify whether a set of three angles can actually form a triangle. The calculator handles both tasks: leave one angle empty to compute it, or enter all three to check validity. It also classifies the result as acute, right, or obtuse.
How to use the calculator - step by step
Enter two known angles (e.g. alpha = 45, beta = 65). Leave the third field empty. Click Calculate. The tool returns gamma = 70 degrees and tells you the triangle is acute.
Enter all three angles (e.g. 90, 45, 45). The calculator checks whether they sum to 180 and classifies the triangle as right, acute, or obtuse. If the sum is not 180, it flags the set as invalid.
The result tells you whether the triangle is acute (all angles below 90 degrees), right (one angle is exactly 90 degrees), or obtuse (one angle exceeds 90 degrees).
Triangle classification reference
| Type | Angle condition | Classic examples |
|---|---|---|
| Acute | All three angles < 90 degrees | 60-60-60 (equilateral), 50-60-70 |
| Right | Exactly one angle = 90 degrees | 90-45-45, 90-60-30 |
| Obtuse | One angle > 90 degrees | 120-30-30, 100-50-30 |
Special triangles you should know
| Triangle | Angles | Side ratios | Where it appears |
|---|---|---|---|
| Equilateral | 60-60-60 | 1 : 1 : 1 | Trusses, road signs, hexagons |
| 45-45-90 | 45-45-90 | 1 : 1 : sqrt(2) | Square diagonal, set squares |
| 30-60-90 | 30-60-90 | 1 : sqrt(3) : 2 | Half of equilateral, drafting |
| 3-4-5 right | ~37-53-90 | 3 : 4 : 5 | Construction, checking right angles |
Real-world scenarios
A roof has a 90-degree angle at the peak support and a 22.5-degree slope on one side. The third angle at the eave is 180 - 90 - 22.5 = 67.5 degrees. Knowing this helps carpenters cut rafters at the correct angle.
A pilot flies from A to B (bearing 040 degrees) then turns toward C. The angle at B in triangle ABC is measured as 75 degrees. If the angle at A is 55 degrees, then the angle at C = 180 - 55 - 75 = 50 degrees. This determines the shape of the flight triangle and helps estimate the return leg distance.
A graphic designer creates a triangular logo with angles of 40 and 100 degrees. The third angle must be 40 degrees, making it isosceles (two equal angles). The designer now knows two sides of the triangle will be equal length, which affects the visual balance.
A surveyor measures two angles of a triangular plot as 63.5 and 48.2 degrees. The third angle = 180 - 63.5 - 48.2 = 68.3 degrees. All three are acute, confirming the plot is a standard shape without extreme narrow corners.
Three forces in equilibrium form a closed triangle. If the angle between forces A and B is 110 degrees, and between B and C is 35 degrees, then the angle between C and A = 35 degrees. This obtuse triangle tells the physicist that one force dominates in direction.
A student measures all three angles of a triangle: 58, 64, and 59. Sum = 181 degrees, which exceeds 180. The calculator flags this as invalid, alerting the student that at least one measurement has an error of about 1 degree.
Why do the angles always sum to 180?
Draw a line through one vertex parallel to the opposite side. The three angles at that vertex (the interior angle plus the two alternate interior angles) form a straight line, which measures 180 degrees. Because alternate interior angles are equal to the angles of the triangle at the other two vertices, the sum of the three interior angles must be 180 degrees. This proof assumes Euclidean (flat) geometry. On a sphere, triangle angles sum to more than 180 degrees; in hyperbolic geometry, they sum to less.
Frequently asked questions
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