If two sides of a triangle are unequal,
then opposite angle of larger side is :

Question

If two sides of a triangle are unequal,
 then opposite angle of larger side is :

Accepted Answer

Explanation:

1. **Why Option 1 is Correct (Greater):**
   - In a triangle, the side opposite the larger angle is always longer. This is a fundamental property of triangles and is derived from the triangle inequality theorem. When two sides of a triangle are unequal, the angle opposite the longer side must be greater than the angle opposite the shorter side. This is because the larger angle allows for a longer span between the two sides that form it, thus making the opposite side longer. Therefore, the angle opposite the larger side is greater.

2. **Why Option 2 is Incorrect (Small):**
   - If the angle opposite the larger side were smaller, it would contradict the basic properties of triangles. A smaller angle would result in a shorter opposite side, not a longer one. Hence, the angle opposite the larger side cannot be smaller.

3. **Why Option 3 is Incorrect (Equal):**
   - If the angles were equal, the sides opposite those angles would also be equal, according to the properties of isosceles triangles. However, the question specifies that the sides are unequal, so the angles cannot be equal.

4. **Why Option 4 is Incorrect (Half):**
   - There is no geometric principle that states the angle opposite a larger side is half of any other angle in the triangle. Angles in a triangle are determined by the relative lengths of the sides, but they do not have a direct half relationship. Therefore, the angle opposite the larger side cannot be half of another angle.

In conclusion, based on the properties of triangles, the angle opposite the larger side is indeed greater, making Option 1 the correct choice.