Use Calculator to Find O in Degrees

Angle O is a fundamental geometric concept used in triangles, polygons, and various geometric calculations. This guide explains how to find angle O in degrees using our interactive calculator and provides practical examples.

What is Angle O?

Angle O refers to an angle in a geometric figure, typically labeled with the letter "O" to distinguish it from other angles. Angles are measured in degrees, with a full circle being 360 degrees. Angle O can appear in various geometric shapes, including triangles, quadrilaterals, and polygons.

In geometry, angles are formed by two rays (the sides of the angle) sharing a common endpoint called the vertex. Angle O is often used in problems involving the sum of angles in a triangle, the exterior angle theorem, or the properties of polygons.

How to Calculate Angle O

Calculating angle O depends on the specific geometric context. Here are the common methods:

In a triangle: The sum of angles in a triangle is always 180 degrees. If you know two angles, you can find the third.
Using the exterior angle theorem: An exterior angle of a triangle is equal to the sum of the two opposite interior angles.
In polygons: The sum of the exterior angles of any polygon is always 360 degrees.

Formula for Angle O in a Triangle

If angle O is the third angle in a triangle with angles A and B known:

O = 180° - (A + B)

Our calculator uses these formulas to compute angle O based on the given inputs.

Angle O in Triangles

In a triangle, angle O is one of the three interior angles. The sum of all three angles in any triangle is always 180 degrees. This property is known as the Triangle Angle Sum Theorem.

Example: If angle A is 60° and angle B is 70°, then angle O would be 180° - (60° + 70°) = 50°.

This property is essential in solving various geometric problems, such as finding missing angles or determining the type of triangle (acute, right, or obtuse).

Angle O in Polygons

In polygons with more than three sides, angle O can refer to an interior or exterior angle. The sum of the exterior angles of any polygon is always 360 degrees, regardless of the number of sides.

Formula for Exterior Angle of a Regular Polygon

For a regular polygon with n sides:

Exterior Angle = 360° / n

For interior angles, the formula depends on the number of sides. For example, in a regular pentagon (n=5), each interior angle is 108°.

Common Angle O Calculations

Here are some typical scenarios where angle O calculations are needed:

Scenario	Calculation Method	Example
Finding a missing angle in a triangle	180° - (angle A + angle B)	If A=40° and B=60°, O=80°
Exterior angle of a triangle	Sum of two opposite interior angles	If A=50° and B=60°, exterior angle O=110°
Interior angle of a regular pentagon	(n-2) × 180° / n	For n=5, each interior angle is 108°

FAQ

What is angle O in geometry?: Angle O is an angle in a geometric figure, typically labeled with the letter "O" to distinguish it from other angles. It can appear in triangles, polygons, and other geometric shapes.
How do I calculate angle O in a triangle?: In a triangle, angle O can be calculated using the formula: O = 180° - (angle A + angle B). You need to know the measures of two other angles to find the third.
What is the sum of all angles in a triangle?: The sum of all angles in any triangle is always 180 degrees. This is known as the Triangle Angle Sum Theorem.
How do I find the exterior angle of a triangle?: The exterior angle of a triangle is equal to the sum of the two opposite interior angles. For example, if angle A is 50° and angle B is 60°, the exterior angle O would be 110°.
What is the sum of the exterior angles of any polygon?: The sum of the exterior angles of any polygon is always 360 degrees, regardless of the number of sides.