Answer
The sum of the measures of all the angles of the given quadrilateral is more than \[{{360}^{\circ }}\].
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.In one of these geometries, called elliptic geometry, it is assumed 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\[{{180}^{\circ }}\].
The sum of the measures of all the angles of any shape is more than that in the Euclidean geometry. As the given figure shows a quadrilateral drawn on a sphere, it is a case of elliptic geometry. So, the sum of the measures of all the angles of the quadrilateral in the figure is more than \[{{360}^{\circ }}\].
