Give an equation for the following statement in general form:
The sum of the angles of a triangle is 180º and two angles are equal to each other.
(Take equal angles to be x and other angle to be y.)
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Answer:
In a Euclidean space, the sum of angles of a triangle equals the straight angle (180 degrees, π radians, two right angles, or a half-turn). A triangle has three angles, one at each vertex, bounded by a pair of adjacent sides.
It was unknown for a long time whether other geometries exist, for which this sum is different. The influence of this problem on mathematics was particularly strong during the 19th century. Ultimately, the answer was proven to be positive: in other spaces (geometries) this sum can be greater or lesser, but it then must depend on the triangle. Its difference from 180° is a case of angular defect and serves as an important distinction for geometric systems.
Equivalence of the parallel postulate and the "sum of the angles equals to 180°" statement
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