Triangle Angle
Find the missing third angle of any triangle from two known angles using the triangle sum theorem (sum = 180 deg). Free online geometry calculator for instant angle results.
About This Calculator
This free online triangle angle calculator finds the missing third angle of any triangle when two angles are known. Simply enter angles A and B in degrees, and the calculator applies the triangle sum theorem to compute angle C = 180 deg - A - B. It also validates whether the three angles form a valid triangle, ensuring each angle is greater than 0 deg and less than 180 deg and that they sum to exactly 180 deg.
The triangle sum theorem is one of the most fundamental rules in geometry: the three interior angles of any triangle always add up to 180 deg (or pi radians). This theorem holds true for all triangles -- acute triangles (all angles less than 90 deg), right triangles (one angle exactly 90 deg), and obtuse triangles (one angle greater than 90 deg). By entering any two known angles, you can instantly determine the third angle and confirm the triangle's validity.
Triangles are classified by their angles into three main types: acute triangles have all three angles less than 90 deg, right triangles have exactly one 90 deg angle, and obtuse triangles have one angle greater than 90 deg. The triangle sum theorem ensures that at most one angle in any triangle can be 90 deg or greater, otherwise the sum would exceed 180 deg.
This triangle angle calculator is ideal for students learning geometry, preparing for exams, or studying angle relationships and triangle classification. It is also useful for professionals in architecture, engineering, design, and construction who need quick and accurate angle calculations for their projects. The calculator provides instant results with two decimal place precision and clearly indicates whether the entered angles form a valid triangle.
The triangle sum theorem is applied universally across all regions and educational systems. Students in India (CBSE, ICSE), the United States (Common Core), and the United Kingdom (GCSE) all learn this fundamental geometric principle. Whether you are solving homework problems, designing a truss structure, or verifying angle measurements in a construction project, this calculator delivers reliable results instantly and is completely free to use.
Frequently Asked Questions
How do I find the missing angle of a triangle?
Add the two known angles together, then subtract the sum from 180 deg. The result is the measure of the third angle. For example, if angles A = 50 deg and B = 60 deg, then angle C = 180 deg - 50 deg - 60 deg = 70 deg.
What is the triangle sum theorem?
The triangle sum theorem states that the sum of the three interior angles of any triangle always equals 180 deg (or pi radians). This holds true for all triangles: acute, right, or obtuse.
Can a triangle have two right angles?
No, a triangle cannot have two right angles (90 deg each) because the sum would already be 180 deg, leaving 0 deg for the third angle. A triangle can have at most one right or one obtuse angle.
How do I know if three angles form a valid triangle?
Three angles form a valid triangle if they sum to exactly 180 deg and each angle is greater than 0 deg and less than 180 deg. The calculator will tell you if the triangle is valid and display the angle sum for verification.
What are interior and exterior angles?
Interior angles are the angles inside the triangle that sum to 180 deg. Each exterior angle is supplementary to its adjacent interior angle (sum = 180 deg), and the sum of all three exterior angles is 360 deg.
What types of triangles are there based on angles?
Triangles are classified by angles into three types: acute triangles have all angles less than 90 deg, right triangles have one angle exactly 90 deg, and obtuse triangles have one angle greater than 90 deg. The triangle sum theorem guarantees at most one angle can be 90 deg or greater.
Can a triangle have all angles less than 60 deg?
No, if all three angles were less than 60 deg, their sum would be less than 180 deg, which violates the triangle sum theorem. At least one angle in any triangle must be 60 deg or greater, and the smallest possible angle approaches 0 deg in a degenerate triangle.
Is this calculator free to use?
Yes, all calculators on Calculy are completely free to use with no registration or download required. You can access the triangle angle calculator from any device with an internet connection.