Answer
The given statement: “In non-Euclidean geometries, the sum of the measures of the angles of a triangle is not necessarily 180°.” is true.
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 .
But, in the non-Euclidean geometries, this assumption is not taken into consideration. So, the sum of the measures of the angles of a triangle is not necessarily .It can either be more than or less than .
Hence, the given statement is true.
