Answer
The sum of the measures of all the angles of the given triangle is more than \[{{180}^{\circ }}\].
Work Step by Step
According to Euclidean geometry, it is assumed that if a line is given and a point taken, which is not on the line, there can only be one line that passes through that point and is parallel to the given line.
This assumption is used to prove that the sum of the measures of all the angles in a triangle is\[{{180}^{\circ }}\]. But, in the non-Euclidean geometries, this assumption is not taken into consideration. One of these geometries, called elliptic geometry, assumes that there are no parallel lines. Elliptic geometry is on a sphere and the sum of the measures of the angles of a triangle is more than\[{{180}^{\circ }}\].
As the given figure shows that the triangle is drawn on a sphere, it is a case of elliptic geometry. So, the sum of the measures of all the angles of the triangle in the figure is more than\[{{180}^{\circ }}\]
