Respuesta :
Answer:
The range for the measure of the third angle is
82° < x ≤ 180°
That is, the third angle is between 82° and 180° (180° inclusive).
Step-by-step explanation:
A spherical triangle is formed on the surface of a sphere by using three great circular arcs intersecting pairwise in three vertices. The spherical triangle is the spherical equivalent of the planar triangle. It is also referred to as the Euler triangle.
The sum of the angles of a spherical triangle is between 180° and 540°. That is, the sum of angles in a spherical triangle must be more than 180° but less than 540°. And the maximum value each angle of a spherical triangle can take on is 180°.
Two angles of a spherical triangle measure 36° and 62°.
Let the third angle be x.
180° < (36° + 62° + x) < 540°
180° < (98° + x) < 540°
Subtracting 98° From the three terms
(180° - 98°) < (98° + x - 98°) < (540° - 98°)
82° < x < 442°
The maximum value each angle of a spherical triangle can take on is 180°, hence, the range of values for this third angle is
82° < x ≤ 180°
Hope this Helps!!!
