Understanding the Third Angles Theorem & Its Application in Triangle Geometry

Third Angles Theorem

The Third Angles Theorem is a property of triangles in Euclidean geometry

The Third Angles Theorem is a property of triangles in Euclidean geometry. It states that if two angles of a triangle are known and their measures add up to less than 180 degrees, then the measure of the third angle is equal to the difference between 180 degrees and the sum of the other two angles.

Mathematically, if a triangle has angles A, B, and C, where angle A and angle B are known and their measures add up to less than 180 degrees, then the measure of angle C is given by:

angle C = 180° – (angle A + angle B)

This theorem is based on the fact that the sum of the angles in any triangle is always 180 degrees. It can be used to find the measure of an unknown angle in a triangle when the measures of the other two angles are known.

For example, let’s say we have a triangle with angle A measuring 30 degrees and angle B measuring 60 degrees. We can use the Third Angles Theorem to find the measure of angle C:

angle C = 180° – (30° + 60°)
angle C = 180° – 90°
angle C = 90°

Therefore, in this triangle, angle C measures 90 degrees.

The Third Angles Theorem is a fundamental concept in triangle geometry and is used in various geometric proofs and calculations involving triangles.

More Answers: