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.

Question

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.

Accepted Answer

Let's analyze each statement:

(a) Sum of interior angles is 180°: This is a fundamental property of triangles in Euclidean geometry. So, (a) is true.

(b) All interior angles can't be equal: This is false because an equilateral triangle has all three interior angles equal to 60°.

(c) Can have at the most one obtuse angle: A triangle can have at most one obtuse angle because having two obtuse angles would exceed the total 180° sum. So, (c) is true.

(d) Sum of two sides may or may not be equal to the third side: This is false because in a triangle, the sum of any two sides must be strictly greater than the third side (triangle inequality). It cannot be equal.

Therefore, only statements (a) and (c) are true, making option 4 the correct answer.

Answer

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