one of the angles of the triangle is equal to thesum of the other two sides of the triangle.find the measure of this triangle
Answers
Answer:
Step-by-step explanation:
If one angle of a triangle is equal to the sum of other two, show that the triangle is a right triangle.
Step-by-step explanation:
"Triangle postulate" redirects here. It is not to be confused with Triangle inequality.
"Angle sum theorem" redirects here. For trigonometric identities concerning sums of angles, see List of trigonometric identities § Angle sum and difference identities.
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