For triangles, which of the following statement(s) are true?
(a) Sum of interior angles is 180°.
(b) All interior angles can’t be equal.
(c) Can have at the most one obtuse angle.
(d) Sum of two sides may or may not be equal to the third side.
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. (a) and (c).
(a) Sum of interior angles is 180°.
This is a fundamental theorem of Euclidean geometry and it is true.
(b) All interior angles can’t be equal.
This is false. An equilateral triangle has three equal angles of 60° each.
(c) Can have at the most one obtuse angle.
This is true. An obtuse angle is greater than 90°. If a triangle had two obtuse angles, its sum would already be greater than 180°, violating the rule that the sum of interior angles is 180°.
(d) Sum of two sides may or may not be equal to the third side.
This is false. The triangle inequality theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Therefore, the correct statements are (a) and (c).